puzzles by topic in Notes

# Puzzles by Topic

The purpose of this page is to sort the puzzles by the techniques needed to solve them. The various techniques are grouped into categories and ordered roughly by complexity. Alongside each technique are the puzzles that can be solved using (primarily) just that technique. Then at the end of each category there is a list of those puzzles that just use techniques from that category. Finally, there is a list of those puzzles that use techniques from that category and earlier categories.

Puzzles may appear more than once as they can have multiple ways of being solved. The categorisation is somewhat arbitrary and depends on what I felt was the primary techniques used in a solution. If a solution used an advanced technique, I probably didn't regard simple concepts as being noteworthy.

In the endnotes for the page for each topic is a list of the pages that link to it. Any that end in _solution_ or _techniques_ indicate a puzzle page. If mentioned in the _techniques_ page then I've classified it as a key technique. If just in the _solution_ page then I've needed it in a solution but have not regarded it as sufficient to note in the listed techniques. This list is automatically generated by the wiki software and sometimes is not complete.

## Basic Angles
* [[angles on a straight line]] 

* [[angles at a point]] 

* [[vertically opposite]] 


## Angles in Parallel Lines
* [[angles and parallel lines]] 


## Shapes
* [[triangle]] 

   <a href="four aligned squares"><img src="/notes/files/FourAlignedSquares_small.png" style="width: 10%"></a><a href="angle formed by three rectangles"><img src="/notes/files/AngleFormedbyThreeRectangles_small.png" style="width: 10%"></a><a href="two triangles in a rectangle"><img src="/notes/files/TwoTrianglesinaRectangle_small.png" style="width: 10%"></a><a href="five squares ii"><img src="/notes/files/FiveSquaresII_small.jpeg" style="width: 10%"></a><a href="subdivided hexagon"><img src="/notes/files/SubdividedHexagon_small.png" style="width: 10%"></a><a href="triangle over two rectangles"><img src="/notes/files/TriangleOverTwoRectangles_small.png" style="width: 10%"></a><a href="subdivided decagon"><img src="/notes/files/SubdividedDecagon_small.png" style="width: 10%"></a><a href="two neighbouring rectangles"><img src="/notes/files/TwoNeighbouringRectangles_small.png" style="width: 10%"></a><a href="striped dodecagon"><img src="/notes/files/StripedDodecagon_small.png" style="width: 10%"></a><a href="two squares in a triangle"><img src="/notes/files/TwoSquaresinaTriangle_small.png" style="width: 10%"></a><a href="three semi-circles around a triangle"><img src="/notes/files/ThreeSemiCirclesAroundaTriangle_small.png" style="width: 10%"></a><a href="three adjacent triangles"><img src="/notes/files/ThreeAdjacentTriangles_small.png" style="width: 10%"></a><a href="four squares around a quadrilateral"><img src="/notes/files/FourSquaresAroundaQuadrilateral_small.png" style="width: 10%"></a>
* [[equilateral triangle]] 

   <a href="two circles inscribed in triangles in a semi-circle"><img src="/notes/files/TwoCirclesInscribedinTrianglesinaSemiCircle_small.png" style="width: 10%"></a><a href="four equilateral triangles round a square"><img src="/notes/files/FourEquilateralTranglesRoundaSquare_small.png" style="width: 10%"></a><a href="stacked shapes"><img src="/notes/files/StackedShapes_small.png" style="width: 10%"></a><a href="four equilateral triangles"><img src="/notes/files/FourEquilateralTriangles_small.jpg" style="width: 10%"></a><a href="two circles in an equilateral triangle"><img src="/notes/files/TwoCirclesinanEquilateralTriangle_small.png" style="width: 10%"></a><a href="two circles in a triangle ii"><img src="/notes/files/TwoCirclesinaTriangleII_small.png" style="width: 10%"></a><a href="two triangles and three concentric semi-circles"><img src="/notes/files/TwoTrianglesandThreeConcentricSemiCircles_small.png" style="width: 10%"></a><a href="diagonal in a square"><img src="/notes/files/DiagonalinaSquare_small.png" style="width: 10%"></a><a href="angle formed by two squares"><img src="/notes/files/AngleFormedbyTwoSquares_small.png" style="width: 10%"></a><a href="circle in triangle in square"><img src="/notes/files/CircleinTriangleinSquare_small.png" style="width: 10%"></a><a href="inverse star in a rectangle"><img src="/notes/files/InverseStarinaRectangle_small.png" style="width: 10%"></a><a href="two triangles overlapping a rectangle"><img src="/notes/files/TwoTrianglesOverlappingaRectangle_small.png" style="width: 10%"></a><a href="nested circles and a triangle"><img src="/notes/files/NestedCirclesandaTriangle_small.png" style="width: 10%"></a><a href="equilateral triangles in a square"><img src="/notes/files/EquilateralTrianglesinaSquare_small.png" style="width: 10%"></a><a href="four circles in a triangle in a circle"><img src="/notes/files/FourCirclesinaTriangleinaCircle_small.png" style="width: 10%"></a>
* [[isosceles triangle]] 

   <a href="angle formed by two squares ii"><img src="/notes/files/AngleFormedbyTwoSquaresII_small.png" style="width: 10%"></a><a href="inverse star in a rectangle"><img src="/notes/files/InverseStarinaRectangle_small.png" style="width: 10%"></a>
* [[right-angled triangle]] 

* [[square]] 

   <a href="two circles inside a square"><img src="/notes/files/TwoCirclesInsideaSquare_small.png" style="width: 10%"></a><a href="concentric semi-circles"><img src="/notes/files/ConcentricSemiCircles_small.png" style="width: 10%"></a><a href="four squares in a big square"><img src="/notes/files/FourSquaresinaBigSquare_small.png" style="width: 10%"></a><a href="stacked squares inside two squares"><img src="/notes/files/StackedSquaresInsideTwoSquares_small.png" style="width: 10%"></a><a href="two squares and a rectangle in an octagon"><img src="/notes/files/TwoSquaresandaRectangleinanOctagon_small.png" style="width: 10%"></a><a href="two circles, two squares"><img src="/notes/files/TwoCirclesTwoSquares_small.png" style="width: 10%"></a><a href="three squares on a line"><img src="/notes/files/ThreeSquaresonaLine_small.png" style="width: 10%"></a><a href="square in a circle in a quarter circle in a square"><img src="/notes/files/SquareinaCircleinaQuarterCircleinaSquare_small.png" style="width: 10%"></a><a href="five rectangles in a square"><img src="/notes/files/FiveRectanglesinaSquare_small.png" style="width: 10%"></a>
* [[rectangle]] 

   <a href="five rectangles tiling a square"><img src="/notes/files/FiveRectanglesTilingaSquare_small.png" style="width: 10%"></a><a href="overlapping triangles"><img src="/notes/files/OverlappingTriangles_small.png" style="width: 10%"></a>
* [[parallelogram]] 

   <a href="tilted rectangles"><img src="/notes/files/TiltedRectangles_small.png" style="width: 10%"></a>
* [[trapezium]] 

   <a href="bell-ringing braids"><img src="/notes/files/BellRingingBraids_small.png" style="width: 10%"></a><a href="triangles formed from rectangles"><img src="/notes/files/TrianglesFormedfromRectangles_small.png" style="width: 10%"></a><a href="areas in a crossed trapezium"><img src="/notes/files/AreasinaCrossedTrapezium_small.png" style="width: 10%"></a><a href="crossed hexagon"><img src="/notes/files/CrossedHexagon_small.png" style="width: 10%"></a>
* [[quadrilateral]] 

* [[angles of a polygon]] 

* [[pentagon]] 

   <a href="circle in pentagon in semi-circle"><img src="/notes/files/CircleInPentagoninSemiCircle_small.png" style="width: 10%"></a>
* [[hexagon]] 

   <a href="three overlapping hexagons"><img src="/notes/files/ThreeOverlappingHexagons_small.png" style="width: 10%"></a><a href="six semi-circles inside a hexagon"><img src="/notes/files/SixSemiCirclesInsideaHexagon_small.png" style="width: 10%"></a><a href="three circles in a hexagon in a circle"><img src="/notes/files/ThreeCirclesinaHexagoninaCircle_small.png" style="width: 10%"></a><a href="three hexagons and a rectangle"><img src="/notes/files/ThreeHexagonsandaRectangle_small.png" style="width: 10%"></a><a href="two hexagons and a square"><img src="/notes/files/TwoHexagonsandaSquare_small.png" style="width: 10%"></a><a href="three circles in a semi-circle"><img src="/notes/files/ThreeCirclesinaSemiCircle_small.png" style="width: 10%"></a><a href="two hexagons in a rectangle"><img src="/notes/files/TwoHexagonsinaRectangle_small.png" style="width: 10%"></a><a href="six semi-circles in a circle"><img src="/notes/files/SixSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="three regular hexagons"><img src="/notes/files/ThreeRegularHexagons_small.png" style="width: 10%"></a>
* [[regular polygon]] 

   <a href="two squares inside an equilateral triangle"><img src="/notes/files/TwoSquaresInsideanEquilateralTriangle_small.png" style="width: 10%"></a>
* [[circle]] 

   <a href="multiple semi-circles in a circle"><img src="/notes/files/MultipleSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="multiple semi-circles"><img src="/notes/files/MultipleSemiCircles_small.png" style="width: 10%"></a><a href="squares and a semi-circle"><img src="/notes/files/SquaresandaSemiCircle_small.png" style="width: 10%"></a><a href="two quarter circles and a semi-circle"><img src="/notes/files/TwoQuarterCirclesandaSemiCircle_small.png" style="width: 10%"></a><a href="three congruent triangles in a semi-circle"><img src="/notes/files/ThreeCongruentTrianglesinaSemiCircle_small.png" style="width: 10%"></a><a href="two semi-circles inside a rectangle"><img src="/notes/files/TwoSemiCirclesInsideaRectangle_small.png" style="width: 10%"></a>
* [[sector]] 

* [[lune]] 

   <a href="multiple semi-circles ii"><img src="/notes/files/MultipleSemiCirclesII_small.png" style="width: 10%"></a>
* [[equation of a shape]] 

   <a href="two squares and an equilateral triangle"><img src="/notes/files/TwoSquaresandanEquilateralTriangle_small.png" style="width: 10%"></a>
* Various Shapes

  <a href="triangle in four rectangles"><img src="/notes/files/TriangleinFourRectangles_small.png" style="width: 10%"></a><a href="two isosceles triangles"><img src="/notes/files/TwoIsoscelesTriangles_small.png" style="width: 10%"></a><a href="region of an octagon"><img src="/notes/files/RegionofanOctagon_small.png" style="width: 10%"></a><a href="polygons with equal perimeter"><img src="/notes/files/PolygonswithEqualPerimeter_small.png" style="width: 10%"></a><a href="arcs in a circle"><img src="/notes/files/ArcsinaCircle_small.png" style="width: 10%"></a><a href="divided hexagon"><img src="/notes/files/DividedHexagon_small.png" style="width: 10%"></a><a href="equilateral triangle in a hexagon"><img src="/notes/files/EquilateralTriangleinaHexagon_small.png" style="width: 10%"></a><a href="nested circles and polygons ii"><img src="/notes/files/NestedCirclesandPolygonsII_small.png" style="width: 10%"></a><a href="quadrilateral from two squares in a square"><img src="/notes/files/QuadrilateralfromTwoSquaresinaSquare_small.png" style="width: 10%"></a><a href="shaded spikes in a hexagon"><img src="/notes/files/ShadedSpikesinaHexagon_small.png" style="width: 10%"></a><a href="six squares in a hexagon"><img src="/notes/files/SixSquaresinaHexagon_small.png" style="width: 10%"></a><a href="three squares and an equilateral triangle"><img src="/notes/files/ThreeSquaresandanEquilateralTriangle_small.png" style="width: 10%"></a><a href="three squares iii"><img src="/notes/files/ThreeSquaresIII_small.png" style="width: 10%"></a><a href="two rectangles overlapping a circle"><img src="/notes/files/TwoRectanglesOverlappingaCircle_small.png" style="width: 10%"></a><a href="two quarter circles in a square"><img src="/notes/files/TwoQuarterCirclesinaSquare_small.png" style="width: 10%"></a><a href="two quarter circles in a rectangle"><img src="/notes/files/TwoQuarterCirclesinaSquareII_small.png" style="width: 10%"></a><a href="triangles in a dodecagon"><img src="/notes/files/TrianglesinaDodecagon_small.png" style="width: 10%"></a><a href="triangle and semi-circle in a circle"><img src="/notes/files/TriangleandSemiCircleinaCircle_small.png" style="width: 10%"></a><a href="three congruent rectangles v"><img src="/notes/files/ThreeCongruentRectanglesV_small.jpeg" style="width: 10%"></a><a href="subdivided hexagon ii"><img src="/notes/files/SubdividedHexagonII_small.jpeg" style="width: 10%"></a><a href="two squares and an equilateral triangle ii"><img src="/notes/files/TwoSquaresandanEquilateralTriangleII_small.jpeg" style="width: 10%"></a><a href="a square in a square"><img src="/notes/files/ASquareinaSquare_small.jpeg" style="width: 10%"></a><a href="two squares ii"><img src="/notes/files/TwoSquaresII_small.jpeg" style="width: 10%"></a><a href="four squares and a triangle ii"><img src="/notes/files/FourSquaresandaTriangleII_small.jpeg" style="width: 10%"></a><a href="subdivided hexagon iii"><img src="/notes/files/SubdividedHexagonIII_small.jpeg" style="width: 10%"></a><a href="three regular hexagons ii"><img src="/notes/files/ThreeRegularHexagonsII_small.png" style="width: 10%"></a><a href="four squares x"><img src="/notes/files/FourSquaresX_small.png" style="width: 10%"></a><a href="three squares ii"><img src="/notes/files/ThreeSquaresII_small.png" style="width: 10%"></a><a href="two regular hexagons iii"><img src="/notes/files/TwoRegularHexagonsIII_small.png" style="width: 10%"></a><a href="isosceles and equilateral triangles"><img src="/notes/files/IsoscelesandEquilateralTriangles_small.png" style="width: 10%"></a><a href="a circle and two semi-circles in two hexagons"><img src="/notes/files/ACircleandTwoSemiCirclesinTwoHexagons_small.png" style="width: 10%"></a><a href="two circles inside an equilateral triangle"><img src="/notes/files/TwoCirclesInsideanEquilateralTriangle_small.png" style="width: 10%"></a><a href="two squares"><img src="/notes/files/TwoSquares_small.png" style="width: 10%"></a><a href="three equal angles in a rectangle"><img src="/notes/files/ThreeEqualAnglesinaRectangle_small.png" style="width: 10%"></a><a href="two congruent rectangles in a square"><img src="/notes/files/TwoCongruentRectanglesinaSquare_small.png" style="width: 10%"></a><a href="three regular hexagons iii"><img src="/notes/files/ThreeRegularHexagonsIII_small.png" style="width: 10%"></a><a href="two squares overlapping a third square"><img src="/notes/files/TwoSquaresOverlappingaThirdSquare_small.png" style="width: 10%"></a><a href="a semi-circle and quarter circle in a square"><img src="/notes/files/ASemiCircleandQuarterCircleinaSquare_small.png" style="width: 10%"></a><a href="overlapping triangle and hexagon"><img src="/notes/files/OverlappingTriangleandHexagon_small.png" style="width: 10%"></a><a href="divided hexagon ii"><img src="/notes/files/DividedHexagonII_small.png" style="width: 10%"></a><a href="quartered hexagon"><img src="/notes/files/QuarteredHexagon_small.png" style="width: 10%"></a><a href="overlapping hexagons"><img src="/notes/files/OverlappingHexagons_small.png" style="width: 10%"></a><a href="three rectangles as a triangle"><img src="/notes/files/ThreeRectanglesasaTriangle_small.png" style="width: 10%"></a><a href="triangle centres and square corners"><img src="/notes/files/TriangleCentresandSquareCorners_small.png" style="width: 10%"></a><a href="hexagon and concentric circles"><img src="/notes/files/HexagonandConcentricCircles_small.png" style="width: 10%"></a><a href="dissected hexagon"><img src="/notes/files/DissectedHexagon_small.png" style="width: 10%"></a>
* With previous categories

  <a href="subdivided triangle iii"><img src="/notes/files/SubdividedTriangleIII_small.jpeg" style="width: 10%"></a><a href="two triangles in a square"><img src="/notes/files/TwoTrianglesinaSquare_small.jpeg" style="width: 10%"></a><a href="four rectangles and a hexagon"><img src="/notes/files/FourRectanglesandaHexagon_small.png" style="width: 10%"></a><a href="a hexagon and a nonagon"><img src="/notes/files/AHexagonandaNonagon_small.png" style="width: 10%"></a><a href="multiple angles"><img src="/notes/files/MultipleAngles_small.png" style="width: 10%"></a><a href="four triangles in a square"><img src="/notes/files/FourTrianglesinaSquare_small.png" style="width: 10%"></a><a href="three isoscelese triangles inside a triangle"><img src="/notes/files/ThreeIsosceleseTrianglesInsideaTriangle_small.png" style="width: 10%"></a><a href="three congruent triangles ii"><img src="/notes/files/ThreeCongruentTrianglesII_small.png" style="width: 10%"></a><a href="divided square"><img src="/notes/files/DividedSquare_small.png" style="width: 10%"></a><a href="circles resting on triangles"><img src="/notes/files/CirclesRestingonTriangles_small.png" style="width: 10%"></a><a href="six rectangles"><img src="/notes/files/SixRectangles_small.jpeg" style="width: 10%"></a><a href="triangle in a rectangle"><img src="/notes/files/TriangleinaRectangle_small.png" style="width: 10%"></a><a href="three right-angled triangles"><img src="/notes/files/ThreeRightAngledTriangles_small.png" style="width: 10%"></a><a href="two squares on a hexagon"><img src="/notes/files/TwoSquaresonaHexagon_small.png" style="width: 10%"></a><a href="four squares inside a rectangle"><img src="/notes/files/FourSquaresInsideaRectangle_small.png" style="width: 10%"></a>
## Measures
* [[Pythagoras]] 

   <a href="a square, triangle, and circle in a square"><img src="/notes/files/ASquareTriangleandCircleinaSquare_small.png" style="width: 10%"></a><a href="three aligned squares"><img src="/notes/files/ThreeAlignedSquares_small.png" style="width: 10%"></a><a href="toppled square"><img src="/notes/files/ToppledSquare_small.png" style="width: 10%"></a><a href="five decreasing squares"><img src="/notes/files/FiveDecreasingSquares_small.png" style="width: 10%"></a><a href="four squares vi"><img src="/notes/files/FourSquaresVI_small.png" style="width: 10%"></a><a href="four squares viii"><img src="/notes/files/FourSquaresVIII_small.png" style="width: 10%"></a><a href="semi-circle in a square in a quarter circle"><img src="/notes/files/SemiCircleinaSquareinaQuarterCircle_small.png" style="width: 10%"></a><a href="stacked boxes in circles in squares"><img src="/notes/files/StackedBoxesinCirclesinSquares_small.png" style="width: 10%"></a><a href="three lengths in a semi-circle"><img src="/notes/files/ASemiCircle_small.jpeg" style="width: 10%"></a><a href="squares in an octagon"><img src="/notes/files/SquaresinanOctagon_small.png" style="width: 10%"></a><a href="two concentric circles"><img src="/notes/files/TwoConcentricCircles_small.png" style="width: 10%"></a><a href="four squares and a quarter circle"><img src="/notes/files/FourSquaresandaQuarterCircle_small.png" style="width: 10%"></a><a href="five equilateral triangles"><img src="/notes/files/FiveEquilateralTriangles_small.png" style="width: 10%"></a><a href="five semi-circles"><img src="/notes/files/FiveSemiCircles_small.png" style="width: 10%"></a><a href="three circles and two semi-circles in a circle"><img src="/notes/files/ThreeCirclesandTwoSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="three stacked squares"><img src="/notes/files/ThreeStackedSquares_small.png" style="width: 10%"></a><a href="two semi-circles diagonally across a square"><img src="/notes/files/TwoSemiCirclesDiagonallyAcrossaSquare_small.png" style="width: 10%"></a><a href="three circles forming a triangle"><img src="/notes/files/ThreeCirclesFormingaTriangle_small.png" style="width: 10%"></a><a href="three equal area rectangles"><img src="/notes/files/ThreeEqualAreaRectangles_small.png" style="width: 10%"></a><a href="seven circles"><img src="/notes/files/SevenCircles_small.png" style="width: 10%"></a><a href="three squares in a semi-circle"><img src="/notes/files/ThreeSquaresinaSemiCircle_small.png" style="width: 10%"></a><a href="one rectangle inside another with semi-circles"><img src="/notes/files/OneRectangleInsideAnotherWithSemiCircles_small.png" style="width: 10%"></a><a href="upside-down semi-circles in a semi-circle"><img src="/notes/files/UpsideDownSemiCirclesinaSemiCircle_small.png" style="width: 10%"></a><a href="square, rectangle, and two semi-circles"><img src="/notes/files/SquareRectangleandTwoSemiCircles_small.png" style="width: 10%"></a><a href="two squares and a rectangle in an octagon"><img src="/notes/files/TwoSquaresandaRectangleinanOctagon_small.png" style="width: 10%"></a><a href="overlapping rectangle and semi-circle"><img src="/notes/files/OverlappingRectangleandSemiCircle_small.png" style="width: 10%"></a><a href="rectangles stacked in a semi-circle"><img src="/notes/files/RectanglesStackedinaSemiCircle_small.png" style="width: 10%"></a><a href="five triangles in a rectangle"><img src="/notes/files/FiveTrianglesinaRectangle_small.png" style="width: 10%"></a><a href="semi-circle and tangents in a square"><img src="/notes/files/SemiCircleandTangentsinaSquare_small.png" style="width: 10%"></a><a href="chord and annulus"><img src="/notes/files/ChordandAnnulus_small.png" style="width: 10%"></a><a href="five overlapping circles"><img src="/notes/files/FiveOverlappingCircles_small.png" style="width: 10%"></a>
* [[area]] 

   <a href="two rectangles in a square"><img src="/notes/files/TwoRectanglesinaSquare_small.png" style="width: 10%"></a><a href="six triangles in a hexagon"><img src="/notes/files/SixTrianglesinaHexagon_small.png" style="width: 10%"></a>
* [[Heron's formula]] 

* [[dissection]] 

   <a href="five decreasing squares"><img src="/notes/files/FiveDecreasingSquares_small.png" style="width: 10%"></a><a href="four squares"><img src="/notes/files/FourSquares_small.png" style="width: 10%"></a><a href="subdivided circles"><img src="/notes/files/SubdividedCircles_small.png" style="width: 10%"></a><a href="three overlapping hexagons"><img src="/notes/files/ThreeOverlappingHexagons_small.png" style="width: 10%"></a><a href="triangle over two rectangles"><img src="/notes/files/TriangleOverTwoRectangles_small.png" style="width: 10%"></a><a href="rectangle on a hexagon"><img src="/notes/files/RectangleonaHexagon_small.png" style="width: 10%"></a><a href="semi-circles in a square"><img src="/notes/files/SemiCirclesinaSquare_small.png" style="width: 10%"></a>
* [[gradients]] 

* [[parallelogram law]] 

   <a href="five semi-circles"><img src="/notes/files/FiveSemiCircles_small.png" style="width: 10%"></a>
* [[parallelogram identity]] 

* With previous categories

  <a href="subdivided triangle"><img src="/notes/files/SubdividedTriangle_small.png" style="width: 10%"></a><a href="squares meeting in a circle"><img src="/notes/files/SquaresMeetinginaCircle_small.png" style="width: 10%"></a><a href="multiple semi-circles iv"><img src="/notes/files/MultipleSemiCirclesIV_small.png" style="width: 10%"></a><a href="overlapping squares"><img src="/notes/files/OverlappingSquares_small.png" style="width: 10%"></a><a href="shaded spikes in a hexagon"><img src="/notes/files/ShadedSpikesinaHexagon_small.png" style="width: 10%"></a><a href="square in a triangle in a square"><img src="/notes/files/SquareinaTriangleinaSquare_small.png" style="width: 10%"></a><a href="three triangles in a square"><img src="/notes/files/ThreeTrianglesinaSquare_small.png" style="width: 10%"></a><a href="two squares and an equilateral triangle ii"><img src="/notes/files/TwoSquaresandanEquilateralTriangleII_small.jpeg" style="width: 10%"></a><a href="three quarter circles ii"><img src="/notes/files/ThreeQuarterCirclesII_small.jpeg" style="width: 10%"></a><a href="a semi-circle and a quarter circle in a rectangle"><img src="/notes/files/ASemiCircleandaQuarterCircleinaRectangle_small.jpeg" style="width: 10%"></a><a href="four houses in a semi-circle"><img src="/notes/files/FourHousesinaSemiCircle_small.jpeg" style="width: 10%"></a><a href="two squares and a quarter circle"><img src="/notes/files/TwoSquaresandaQuarterCircle_small.jpeg" style="width: 10%"></a><a href="two semi-circles and two quarter circles"><img src="/notes/files/TwoSemiCirclesandTwoQuarterCircles_small.jpeg" style="width: 10%"></a><a href="three semi-circles in a rectangle"><img src="/notes/files/ThreeSemiCirclesinaRectangle_small.jpeg" style="width: 10%"></a><a href="subdivided semi-circle"><img src="/notes/files/SubdividedSemiCircle_small.jpeg" style="width: 10%"></a><a href="two squares iii"><img src="/notes/files/TwoSquaresIII_small.jpeg" style="width: 10%"></a><a href="three squares vi"><img src="/notes/files/ThreeSquaresVI_small.jpeg" style="width: 10%"></a><a href="two quarter circles and a circle"><img src="/notes/files/TwoQuarterCirclesandaCircle_small.jpeg" style="width: 10%"></a><a href="two squares and two equilateral triangles ii"><img src="/notes/files/TwoSquaresandTwoEquilateralTrianglesII_small.png" style="width: 10%"></a><a href="two squares and two equilateral triangles iii"><img src="/notes/files/TwoSquaresandTwoEquilateralTrianglesIII_small.png" style="width: 10%"></a><a href="six squares in a semi-circle and a quarter circle"><img src="/notes/files/TwoRectanglesandaSquareII_small.jpeg" style="width: 10%"></a><a href="two octagons and two squares"><img src="/notes/files/TwoOctagonsandTwoSquares_small.png" style="width: 10%"></a><a href="subdivided triangle ii"><img src="/notes/files/SubdividedTriangleII_small.png" style="width: 10%"></a><a href="four quarter circles ii"><img src="/notes/files/FourQuarterCirclesII_small.png" style="width: 10%"></a><a href="two hexagons in a rectangle II"><img src="/notes/files/TwoHexagonsinaRectangleII_small.png" style="width: 10%"></a><a href="five quarter circles"><img src="/notes/files/FiveQuarterCircles_small.png" style="width: 10%"></a><a href="circle inside a triangle"><img src="/notes/files/CircleInsideaTriangle_small.png" style="width: 10%"></a><a href="swirling semi-circles"><img src="/notes/files/SwirlingSemiCircles_small.png" style="width: 10%"></a><a href="four quarter circles"><img src="/notes/files/FourQuarterCircles_small.png" style="width: 10%"></a><a href="two semi-circles and an equilateral triangle"><img src="/notes/files/TwoSemiCirclesandanEquilateralTriangle_small.png" style="width: 10%"></a><a href="five circles in a rectangle in a semi-circle"><img src="/notes/files/FiveCirclesinaRectangleinaSemiCircle_small.png" style="width: 10%"></a><a href="circle in a quarter circle"><img src="/notes/files/CircleinaQuarterCircle_small.png" style="width: 10%"></a><a href="three semi-circles"><img src="/notes/files/ThreeSemiCircles_small.png" style="width: 10%"></a><a href="a square and a rectangle overlapping"><img src="/notes/files/ASquareandaRectangleOverlapping_small.png" style="width: 10%"></a><a href="five semi-circles around a rectangle"><img src="/notes/files/FiveSemiCirclesAroundaRectangle_small.png" style="width: 10%"></a><a href="a square, a circle, and a rectangle"><img src="/notes/files/ASquareACircleandaRectangle_small.png" style="width: 10%"></a><a href="two rectangles overlapping a square"><img src="/notes/files/TwoRectanglesOverlappingaSquare_small.png" style="width: 10%"></a><a href="seven hexagons"><img src="/notes/files/SevenHexagons_small.png" style="width: 10%"></a><a href="a pattern of squares"><img src="/notes/files/APatternofSquares_small.png" style="width: 10%"></a><a href="six circles inside a circle inside a square"><img src="/notes/files/SixCirclesInsideaCircleInsideaSquare_small.png" style="width: 10%"></a><a href="stacked triangles"><img src="/notes/files/StackedTriangles_small.png" style="width: 10%"></a><a href="three parallel semi-circles"><img src="/notes/files/ThreeParallelSemiCircles_small.png" style="width: 10%"></a><a href="triangle overlapping a hexagon"><img src="/notes/files/TriangleOverlappingaHexagon_small.png" style="width: 10%"></a><a href="three overlapping circles"><img src="/notes/files/ThreeOverlappingCircles_small.png" style="width: 10%"></a><a href="square overlapping a quarter circle"><img src="/notes/files/SquareOverlappingaQuarterCircle_small.png" style="width: 10%"></a><a href="triangle in semi-circle with square"><img src="/notes/files/TriangleinSemiCirclewithSquare_small.png" style="width: 10%"></a><a href="circle in a hexagon in a semi-circle"><img src="/notes/files/CircleinaHexagoninaSemiCircle_small.png" style="width: 10%"></a><a href="circles around a triangle"><img src="/notes/files/CirclesAroundaTriangle_small.png" style="width: 10%"></a><a href="nested circles and polygons"><img src="/notes/files/NestedCirclesandPolygons_small.png" style="width: 10%"></a><a href="arcs inside a triangle"><img src="/notes/files/ArcsInsideaTriangle_small.png" style="width: 10%"></a><a href="spiralling semi-circles"><img src="/notes/files/SpirallingSemiCircles_small.png" style="width: 10%"></a><a href="semi-circle between two quarter circles"><img src="/notes/files/SemiCircleBetweenTwoQuarterCircles_small.png" style="width: 10%"></a>
## Transformations and Symmetry
* [[congruent]] 

   <a href="four quarter circles iii"><img src="/notes/files/FourQuarterCirclesIII_small.png" style="width: 10%"></a><a href="two squares overlapping a square"><img src="/notes/files/TwoSquaresOverlappingaSquare_small.png" style="width: 10%"></a><a href="five congruent rectangles"><img src="/notes/files/FiveCongruentRectangles_small.png" style="width: 10%"></a><a href="three stacked squares and a fourth square"><img src="/notes/files/ThreeStackedSquaresandaFourthSquare_small.png" style="width: 10%"></a><a href="circle and two squares"><img src="/notes/files/CircleandTwoSquares_small.png" style="width: 10%"></a><a href="four regular polygons"><img src="/notes/files/FourRegularPolygons_small.png" style="width: 10%"></a>
* [[similarity]] 

   <a href="concentric semi-circles"><img src="/notes/files/ConcentricSemiCircles_small.png" style="width: 10%"></a><a href="a square and a triangle"><img src="/notes/files/ASquareandaTriangle_small.jpeg" style="width: 10%"></a><a href="four squares and an isosceles triangle"><img src="/notes/files/FourSquaresandanIsoscelesTriangle_small.jpeg" style="width: 10%"></a><a href="five squares"><img src="/notes/files/FiveSquares_small.jpeg" style="width: 10%"></a><a href="two squares overlapping a square ii"><img src="/notes/files/TwoSquaresOverlappingaSquareII_small.png" style="width: 10%"></a><a href="two overlapping triangles"><img src="/notes/files/TwoOverlappingTriangles_small.png" style="width: 10%"></a><a href="rectangle tilted over a square"><img src="/notes/files/RectangleTiltedOveraSquare_small.png" style="width: 10%"></a><a href="two triangles and three concentric semi-circles"><img src="/notes/files/TwoTrianglesandThreeConcentricSemiCircles_small.png" style="width: 10%"></a><a href="two squares diagonally inside a rectangle"><img src="/notes/files/TwoSquaresDiagonallyInsideaRectangle_small.png" style="width: 10%"></a><a href="three overlapping rectangles ii"><img src="/notes/files/ThreeOverlappingRectanglesII_small.png" style="width: 10%"></a><a href="three squares in a triangle"><img src="/notes/files/ThreeSquaresinaTriangle_small.png" style="width: 10%"></a><a href="three circles in a rectangle"><img src="/notes/files/ThreeCirclesinaRectangle_small.png" style="width: 10%"></a><a href="three circles in a rectangle ii"><img src="/notes/files/ThreeCirclesinaRectangleII_small.png" style="width: 10%"></a><a href="three congruent squares in a rectangle"><img src="/notes/files/ThreeCongruentSquaresinaRectangle_small.png" style="width: 10%"></a><a href="overlapping triangle and rectangle"><img src="/notes/files/OverlappingTriangleandRectangle_small.png" style="width: 10%"></a><a href="square with midpoints"><img src="/notes/files/SquarewithMidpoints_small.png" style="width: 10%"></a><a href="quarter circles in a square in a circle"><img src="/notes/files/QuarterCirclesinaSquareinaCircle_small.png" style="width: 10%"></a><a href="semi-circles in a quarter circle"><img src="/notes/files/SemiCirclesinaQuarterCircle_small.png" style="width: 10%"></a><a href="triangles in a semi-circle"><img src="/notes/files/TrianglesinaSemiCircle_small.png" style="width: 10%"></a><a href="three squares in a square"><img src="/notes/files/ThreeSquaresinaSquare_small.png" style="width: 10%"></a>
* [[symmetry]] 

   <a href="three congruent rectangles iv"><img src="/notes/files/ThreeCongruentRectanglesIV_small.png" style="width: 10%"></a><a href="squares in an octagon"><img src="/notes/files/SquaresinanOctagon_small.png" style="width: 10%"></a><a href="two overlapping triangles ii"><img src="/notes/files/TwoOverlappingTrianglesII_small.png" style="width: 10%"></a><a href="four equilateral triangles inside a hexagon"><img src="/notes/files/FourEquilateralTrianglesInsideaHexagon_small.png" style="width: 10%"></a><a href="two quarter circles in a semi-circle ii"><img src="/notes/files/TwoQuarterCirclesinaSemiCircleII_small.png" style="width: 10%"></a><a href="tilted rectangle in a square"><img src="/notes/files/TiltedRectangleinaSquare_small.png" style="width: 10%"></a>
* [[transformation]] 

   <a href="three triangles in a hexagon"><img src="/notes/files/ThreeTrianglesinaHexagon_small.png" style="width: 10%"></a><a href="five squares ii"><img src="/notes/files/FiveSquaresII_small.jpeg" style="width: 10%"></a><a href="hexagon and a square"><img src="/notes/files/HexagonandaSquare_small.png" style="width: 10%"></a><a href="triangle in two tilted squares"><img src="/notes/files/TriangleinTwoTiltedSquares_small.png" style="width: 10%"></a><a href="two squares on a hexagon"><img src="/notes/files/TwoSquaresonaHexagon_small.png" style="width: 10%"></a><a href="two overlapping triangles"><img src="/notes/files/TwoOverlappingTriangles_small.png" style="width: 10%"></a><a href="four squares iii"><img src="/notes/files/FourSquaresIII_small.png" style="width: 10%"></a><a href="angles in two hexagons"><img src="/notes/files/AnglesinTwoHexagons_small.png" style="width: 10%"></a><a href="four hexagons"><img src="/notes/files/FourHexagons_small.png" style="width: 10%"></a><a href="rectangle on a hexagon"><img src="/notes/files/RectangleonaHexagon_small.png" style="width: 10%"></a><a href="four regular polygons"><img src="/notes/files/FourRegularPolygons_small.png" style="width: 10%"></a>
* [[tessellation]] 

   <a href="four squares overlapping a rectangle"><img src="/notes/files/FourSquaresOverlappingaRectangle_small.png" style="width: 10%"></a><a href="three overlapping rectangles"><img src="/notes/files/ThreeOverlappingRectangles_small.png" style="width: 10%"></a><a href="striped hexagon"><img src="/notes/files/StripedHexagon_small.png" style="width: 10%"></a>
* [[bisection]] 

* Various Transformations and Symmetry

  <a href="two rectangles and a square"><img src="/notes/files/TwoRectanglesandaSquare_small.jpeg" style="width: 10%"></a><a href="three squares iv"><img src="/notes/files/ThreeSquaresIV_small.png" style="width: 10%"></a><a href="triangles with a parallelogram"><img src="/notes/files/TriangleswithaParallelogram_small.png" style="width: 10%"></a>
* With previous categories

  <a href="two rectangles of equal area"><img src="/notes/files/TwoRectanglesofEqualArea_small.png" style="width: 10%"></a><a href="crossed hexagon"><img src="/notes/files/CrossedHexagon_small.png" style="width: 10%"></a><a href="rectangle quartered by semi-circles"><img src="/notes/files/RectangleQuarteredbySemiCircles_small.png" style="width: 10%"></a><a href="subdivided parallelogram"><img src="/notes/files/SubdividedParallelogram_small.png" style="width: 10%"></a><a href="two circles in a square"><img src="/notes/files/TwoCirclesinaSquare_small.png" style="width: 10%"></a><a href="hexagon in a star in a hexagon"><img src="/notes/files/HexagoninaStarinaHexagon_small.png" style="width: 10%"></a><a href="stacked hexagons"><img src="/notes/files/StackedHexagons_small.png" style="width: 10%"></a><a href="four squares"><img src="/notes/files/FourSquares_small.png" style="width: 10%"></a><a href="semi-circle on a hexagon"><img src="/notes/files/SemiCircleonaHexagon_small.png" style="width: 10%"></a><a href="three congruent rectangles ii"><img src="/notes/files/ThreeCongruentRectanglesII_small.png" style="width: 10%"></a><a href="striped semi-circle"><img src="/notes/files/StripedSemiCircle_small.png" style="width: 10%"></a><a href="zig-zag triangles"><img src="/notes/files/ZigzagTriangles_small.png" style="width: 10%"></a><a href="two triangles in a rectangle"><img src="/notes/files/TwoTrianglesinaRectangle_small.png" style="width: 10%"></a><a href="two perpendicular equilateral triangles"><img src="/notes/files/TwoPerpendicularEquilateralTriangles_small.png" style="width: 10%"></a><a href="two equilateral triangles ii"><img src="/notes/files/TwoEquilateralTrianglesII_small.jpeg" style="width: 10%"></a><a href="three squares and a rectangle"><img src="/notes/files/ThreeSquaresandaRectangle_small.jpeg" style="width: 10%"></a><a href="five regular polygons"><img src="/notes/files/FiveRegularPolygons_small.jpeg" style="width: 10%"></a><a href="two rectangles"><img src="/notes/files/TwoRectangles_small.jpeg" style="width: 10%"></a><a href="four congruent triangles"><img src="/notes/files/FourCongruentTriangles_small.jpeg" style="width: 10%"></a><a href="four squares and a triangle"><img src="/notes/files/FourSquaresandaTriangle_small.jpeg" style="width: 10%"></a><a href="three squares and a triangle"><img src="/notes/files/ThreeSquaresandaTriangle_small.jpeg" style="width: 10%"></a><a href="three squares"><img src="/notes/files/ThreeSquares_small.png" style="width: 10%"></a><a href="four squares ix"><img src="/notes/files/FourSquaresIX_small.png" style="width: 10%"></a><a href="three congruent rectangles vi"><img src="/notes/files/ThreeCongruentRectanglesVI_small.png" style="width: 10%"></a><a href="three quarter circles"><img src="/notes/files/ThreeQuarterCircles_small.png" style="width: 10%"></a><a href="zig-zag inside a square"><img src="/notes/files/ZigzagInsideaSquare_small.png" style="width: 10%"></a><a href="chord splitting a square in half"><img src="/notes/files/ChordSplittingaSquareinHalf_small.png" style="width: 10%"></a><a href="two congruent rectangles and a semi-circle"><img src="/notes/files/TwoCongruentRectanglesandaSemiCircle_small.png" style="width: 10%"></a><a href="semi-circle splitting a triangle"><img src="/notes/files/SemiCircleSplittingaTriangle_small.png" style="width: 10%"></a><a href="square and rectangle overlapping in a semi-circle"><img src="/notes/files/SquareandRectangleOverlappinginaSemiCircle_small.png" style="width: 10%"></a><a href="parallelogram in a rectangle"><img src="/notes/files/ParallelograminaRectangle_small.png" style="width: 10%"></a><a href="two overlapping hexagons and a rectangle"><img src="/notes/files/TwoOverlappingHexagonsandaRectangle_small.png" style="width: 10%"></a><a href="two congruent quadrilaterals and a rectangle"><img src="/notes/files/TwoCongruentQuadrilateralsandaRectangle_small.png" style="width: 10%"></a><a href="three hexagons in a trapezium"><img src="/notes/files/ThreeHexagonsinaTrapezium_small.png" style="width: 10%"></a><a href="two regular hexagons ii"><img src="/notes/files/TwoRegularHexagonsII_small.png" style="width: 10%"></a><a href="two rectangles with diagonals"><img src="/notes/files/TwoRectangleswithDiagonals_small.png" style="width: 10%"></a><a href="square on an octagon"><img src="/notes/files/SquareonanOctagon_small.png" style="width: 10%"></a><a href="circle and semi-circle in triangle"><img src="/notes/files/CircleandSemiCircleinTriangle_small.png" style="width: 10%"></a><a href="circles in overlapping triangles"><img src="/notes/files/CirclesinOverlappingTriangles_small.png" style="width: 10%"></a><a href="divided hexagon iii"><img src="/notes/files/DividedHexagonIII_small.png" style="width: 10%"></a><a href="three aligned triangles"><img src="/notes/files/ThreeAlignedTriangles_small.png" style="width: 10%"></a><a href="two equilateral triangles in a semi-circle"><img src="/notes/files/TwoEquilateralTrianglesinaSemiCircle_small.png" style="width: 10%"></a><a href="circles in triangle and rhombus"><img src="/notes/files/CirclesinTriangleandRhombus_small.png" style="width: 10%"></a><a href="three congruent triangles"><img src="/notes/files/ThreeCongruentTriangles_small.png" style="width: 10%"></a><a href="two equilateral triangles iii"><img src="/notes/files/TwoEquilateralTrianglesIII_small.jpeg" style="width: 10%"></a><a href="three congruent squares overlapping a square"><img src="/notes/files/ThreeCongruentSquaresOverlappingaSquare_small.png" style="width: 10%"></a><a href="two overlapping squares ii"><img src="/notes/files/TwoOverlappingSquaresII_small.png" style="width: 10%"></a><a href="three squares and two triangles"><img src="/notes/files/ThreeSquaresandTwoTriangles_small.jpeg" style="width: 10%"></a><a href="three regular hexagons iv"><img src="/notes/files/ThreeRegularHexagonsIV_small.jpeg" style="width: 10%"></a><a href="five equilateral triangles ii"><img src="/notes/files/FiveEquilateralTrianglesII_small.jpeg" style="width: 10%"></a><a href="subdivided hexagon iv"><img src="/notes/files/SubdividedHexagonIV_small.jpeg" style="width: 10%"></a><a href="lengths in a crossed trapezium"><img src="/notes/files/LengthsinaCrossedTrapezium_small.png" style="width: 10%"></a><a href="four equilateral triangles"><img src="/notes/files/FourEquilateralTriangles_small.jpg" style="width: 10%"></a><a href="four squares ii"><img src="/notes/files/FourSquaresII_small.png" style="width: 10%"></a><a href="four squares v"><img src="/notes/files/FourSquaresV_small.png" style="width: 10%"></a><a href="three congruent rectangles iii"><img src="/notes/files/ThreeCongruentRectanglesIII_small.png" style="width: 10%"></a><a href="two overlapping squares iii"><img src="/notes/files/TwoOverlappingSquaresIII_small.png" style="width: 10%"></a><a href="three squares viii"><img src="/notes/files/ThreeSquaresVIII_small.jpeg" style="width: 10%"></a><a href="three congruent rectangles"><img src="/notes/files/ThreeCongruentRectangles_small.png" style="width: 10%"></a><a href="three congruent rectangles"><img src="/notes/files/ThreeCongruentRectangles_small.png" style="width: 10%"></a><a href="four squares in a semi-circle"><img src="/notes/files/FourSquaresinaSemiCircle_small.png" style="width: 10%"></a><a href="two semi-circles in a circle"><img src="/notes/files/TwoSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="two tilted squares"><img src="/notes/files/TwoTiltedSquares_small.png" style="width: 10%"></a><a href="two quarter circles in a rectangle in a semi-circle"><img src="/notes/files/TwoQuarterCirclesinaRectangleinaSemiCircle_small.png" style="width: 10%"></a><a href="four congruent squares inside a larger square"><img src="/notes/files/FourCongruentSquaresInsideaLargerSquare_small.png" style="width: 10%"></a><a href="parallelogram area"><img src="/notes/files/ParallelogramArea_small.png" style="width: 10%"></a><a href="parallelogram in a rectangle"><img src="/notes/files/ParallelograminaRectangle_small.png" style="width: 10%"></a><a href="three squares inside a triangle"><img src="/notes/files/ThreeSquaresInsideaTriangle_small.png" style="width: 10%"></a><a href="stack of congruent rectangles"><img src="/notes/files/StackofCongruentRectangles_small.png" style="width: 10%"></a><a href="two overlapping squares"><img src="/notes/files/TwoOverlappingSquares_small.png" style="width: 10%"></a><a href="three tilted rectangles"><img src="/notes/files/ThreeTiltedRectangles_small.png" style="width: 10%"></a><a href="partitioned square"><img src="/notes/files/PartitionedSquare_small.png" style="width: 10%"></a><a href="subdivided square"><img src="/notes/files/SubdividedSquare_small.png" style="width: 10%"></a><a href="three squares vii"><img src="/notes/files/ThreeSquaresVII_small.jpeg" style="width: 10%"></a><a href="three squares and two equilateral triangles"><img src="/notes/files/ThreeSquaresandTwoEquilateralTriangles_small.png" style="width: 10%"></a><a href="hexagon and a square"><img src="/notes/files/HexagonandaSquare_small.png" style="width: 10%"></a><a href="multiple semi-circles iii"><img src="/notes/files/MultipleSemiCirclesIII_small.png" style="width: 10%"></a><a href="five squares across a square"><img src="/notes/files/FiveSquaresAcrossaSquare_small.png" style="width: 10%"></a>
## Circle Theorems
* [[chord]] 

* [[angle between a radius and tangent]] 

   <a href="semi-circle in a right-angled triangle"><img src="/notes/files/SemiCircleinaRightAngledTriangle_small.png" style="width: 10%"></a>
* [[angle in a semi-circle]] 

   <a href="two triangles and a quarter circle"><img src="/notes/files/TwoTrianglesandaQuarterCircle_small.jpeg" style="width: 10%"></a><a href="two squares inside a semi-circle"><img src="/notes/files/TwoSquaresInsideaSemiCircle_small.png" style="width: 10%"></a>
* [[angle at the circumference is half that at the centre]] 

   <a href="rectangle across a rectangle"><img src="/notes/files/RectangleAcrossaSquare_small.png" style="width: 10%"></a><a href="regular hexagon and rectangle"><img src="/notes/files/RegularHexagonandRectangle_small.png" style="width: 10%"></a><a href="three squares iii"><img src="/notes/files/ThreeSquaresIII_small.png" style="width: 10%"></a><a href="two triangles overlapping a quarter circle"><img src="/notes/files/TwoTrianglesOverlappingaQuarterCircle_small.png" style="width: 10%"></a><a href="two regular hexagons"><img src="/notes/files/TwoRegularHexagons_small.png" style="width: 10%"></a><a href="three squares v"><img src="/notes/files/ThreeSquaresV_small.jpeg" style="width: 10%"></a><a href="isosceles and equilateral triangles"><img src="/notes/files/IsoscelesandEquilateralTriangles_small.png" style="width: 10%"></a><a href="two quarter circles in a semi-circle ii"><img src="/notes/files/TwoQuarterCirclesinaSemiCircleII_small.png" style="width: 10%"></a><a href="two hexagons and a triangle"><img src="/notes/files/TwoHexagonsandaTriangle_small.png" style="width: 10%"></a><a href="two squares overlapping a square ii"><img src="/notes/files/TwoSquaresOverlappingaSquareII_small.png" style="width: 10%"></a><a href="three overlapping squares"><img src="/notes/files/ThreeOverlappingSquares_small.png" style="width: 10%"></a><a href="angle formed by two squares ii"><img src="/notes/files/AngleFormedbyTwoSquaresII_small.png" style="width: 10%"></a><a href="tilted triangles"><img src="/notes/files/TiltedTriangles_small.png" style="width: 10%"></a>
* [[angles in the same segment]] 

   <a href="quarter circle overlapping a circle"><img src="/notes/files/QuarterCircleOverlappingaCircle_small.png" style="width: 10%"></a>
* [[cyclic quadrilateral]] 

* [[intersecting chords theorem]] 

   <a href="four stacked squares in a circle in a square"><img src="/notes/files/FourStackedSquaresinaCircleinaSquare_small.png" style="width: 10%"></a><a href="overlapping square and circle"><img src="/notes/files/OverlappingSquareandCircle_small.png" style="width: 10%"></a><a href="chords dividing a triangle into five"><img src="/notes/files/ChordsDividingaTriangleintoFive_small.png" style="width: 10%"></a><a href="two concentric circles"><img src="/notes/files/TwoConcentricCircles_small.png" style="width: 10%"></a><a href="four squares and a semi-circle"><img src="/notes/files/FourSquaresandaSemiCircle_small.png" style="width: 10%"></a><a href="three squares overlapping a semi-circle"><img src="/notes/files/ThreeSquaresOverlappingaSemiCircle_small.png" style="width: 10%"></a><a href="two semi-circles and a rectangle"><img src="/notes/files/TwoSemiCirclesandaRectangle_small.png" style="width: 10%"></a><a href="semi-circle in a circle"><img src="/notes/files/SemiCircleinaCircle_small.png" style="width: 10%"></a><a href="square overlapping a circle"><img src="/notes/files/SquareOverlappingaCircle_small.png" style="width: 10%"></a><a href="chord and annulus"><img src="/notes/files/ChordandAnnulus_small.png" style="width: 10%"></a><a href="arbelos"><img src="/notes/files/Arbelos_small.png" style="width: 10%"></a>
* [[alternate segment theorem]] 

* Various Circle Theorems

  <a href="triangle in circle in triangle in semi-circle"><img src="/notes/files/TriangleinCircleinTriangleinSemiCircle_small.png" style="width: 10%"></a><a href="four squares iv"><img src="/notes/files/FourSquaresIV_small.png" style="width: 10%"></a><a href="two circles"><img src="/notes/files/TwoCircles_small.jpeg" style="width: 10%"></a><a href="two quarter circles"><img src="/notes/files/TwoQuarterCircles_small.jpeg" style="width: 10%"></a><a href="three squares ii"><img src="/notes/files/ThreeSquaresII_small.png" style="width: 10%"></a><a href="two squares on a hexagon"><img src="/notes/files/TwoSquaresonaHexagon_small.png" style="width: 10%"></a><a href="two overlapping triangles"><img src="/notes/files/TwoOverlappingTriangles_small.png" style="width: 10%"></a><a href="multiple angles"><img src="/notes/files/MultipleAngles_small.png" style="width: 10%"></a><a href="two squares on a triangle"><img src="/notes/files/TwoSquaresonaTriangle_small.png" style="width: 10%"></a><a href="two rectangles in a semi-circle"><img src="/notes/files/TwoRectanglesinaSemiCircle_small.png" style="width: 10%"></a>
* With previous categories

  <a href="six squares and a quarter circle"><img src="/notes/files/SixSquaresandaQuarterCircle_small.png" style="width: 10%"></a><a href="four isosceles triangles in a circle"><img src="/notes/files/FourIsoscelesTrianglesinaCircle_small.png" style="width: 10%"></a><a href="semi-circle in a square"><img src="/notes/files/SemiCircleinaSquare_small.png" style="width: 10%"></a><a href="three congruent triangles"><img src="/notes/files/ThreeCongruentTriangles_small.png" style="width: 10%"></a><a href="triangle in a circle in a quarter circle in a square"><img src="/notes/files/TriangleCircleQuarterCircleSquare_small.png" style="width: 10%"></a><a href="three squares in a circle"><img src="/notes/files/ThreeSquaresinaCircle_small.png" style="width: 10%"></a><a href="two semi-circles in an equilateral triangle"><img src="/notes/files/TwoSemiCirclesInanEquilateralTriangle_small.jpeg" style="width: 10%"></a><a href="three regular hexagons and a semi-circle"><img src="/notes/files/ThreeRegularHexagonsandaSemiCircle_small.png" style="width: 10%"></a><a href="triangle over a circle"><img src="/notes/files/TriangleOveraCircle_small.png" style="width: 10%"></a><a href="two circles in a square ii"><img src="/notes/files/TwoCirclesinaSquareII_small.png" style="width: 10%"></a><a href="rectangle overlapping a circle"><img src="/notes/files/RectangleOverlappingaCircle_small.png" style="width: 10%"></a><a href="a square and a hexagon"><img src="/notes/files/ASquareandaHexagon_small.png" style="width: 10%"></a><a href="six equal area rectangles"><img src="/notes/files/SixEqualAreaRectangles_small.png" style="width: 10%"></a><a href="arcs in a semi-circle"><img src="/notes/files/ArcsinaSemiCircle_small.png" style="width: 10%"></a><a href="two squares"><img src="/notes/files/TwoSquares_small.png" style="width: 10%"></a><a href="pentagram in a circle"><img src="/notes/files/PentagraminaCircle_small.png" style="width: 10%"></a><a href="two circles in a rectangle"><img src="/notes/files/TwoCirclesinaRectangle_small.png" style="width: 10%"></a><a href="overlapping triangles in a circle"><img src="/notes/files/OverlappingTrianglesinaCircle_small.png" style="width: 10%"></a><a href="three equilateral triangles and a semi-circle"><img src="/notes/files/ThreeEquilateralTrianglesandaSemiCircle_small.png" style="width: 10%"></a><a href="angles in two circles"><img src="/notes/files/AnglesinTwoCircles_small.png" style="width: 10%"></a><a href="two circles inside two polygons inside a circle"><img src="/notes/files/TwoCirclesInsideTwoPolygonsInsideaCircle_small.png" style="width: 10%"></a><a href="triangle and circle inside square"><img src="/notes/files/TriangleandCircleInsideSquare_small.png" style="width: 10%"></a><a href="pentagon with two semi-circles"><img src="/notes/files/PentagonwithtwoSemiCircles_small.png" style="width: 10%"></a><a href="quarter circles in a rectangle"><img src="/notes/files/QuarterCirclesinaRectangle_small.png" style="width: 10%"></a><a href="tangential hexagon and circle"><img src="/notes/files/TangentialHexagonandCircle_small.png" style="width: 10%"></a><a href="two triangles in a circle and semi-circle"><img src="/notes/files/TwoTrianglesinaCircleandSemiCircle_small.png" style="width: 10%"></a><a href="two overlapping triangles and a circle"><img src="/notes/files/TwoOverlappingTrianglesandaCircle_small.png" style="width: 10%"></a><a href="two overlapping triangles and a circle"><img src="/notes/files/TwoOverlappingTrianglesandaCircle_small.png" style="width: 10%"></a><a href="quadrilateral splitting a semi-circle"><img src="/notes/files/QuadrilateralSplittingaSemiCircle_small.png" style="width: 10%"></a><a href="nested isosceles triangles"><img src="/notes/files/NestedIsoscelesTriangles_small.png" style="width: 10%"></a><a href="angles in a circle"><img src="/notes/files/AnglesinaCircle_small.png" style="width: 10%"></a><a href="angle in a circle and semi-circle"><img src="/notes/files/AngleinaCircleandSemiCircle_small.png" style="width: 10%"></a><a href="four stacked squares in a circle in a square"><img src="/notes/files/FourStackedSquaresinaCircleinaSquare_small.png" style="width: 10%"></a><a href="four squares overlapping a circle"><img src="/notes/files/FourSquaresOverlappingaCircle_small.png" style="width: 10%"></a><a href="four parallel semi-circles"><img src="/notes/files/FourParallelSemiCircles_small.png" style="width: 10%"></a><a href="two squares and a semi-circle"><img src="/notes/files/TwoSquaresandaSemiCircle_small.png" style="width: 10%"></a><a href="two circles in a triangle"><img src="/notes/files/TwoCirclesinaTriangle_small.png" style="width: 10%"></a><a href="a quarter circle and a semi-circle in a triangle"><img src="/notes/files/AQuarterCircleandaSemiCircleinaTriangle_small.jpeg" style="width: 10%"></a><a href="three lengths in a semi-circle"><img src="/notes/files/ASemiCircle_small.jpeg" style="width: 10%"></a><a href="five semi-circles"><img src="/notes/files/FiveSemiCircles_small.png" style="width: 10%"></a><a href="four quarter circles in a circle"><img src="/notes/files/FourQuarterCirclesinaCircle_small.png" style="width: 10%"></a><a href="two semi-circles in a circle"><img src="/notes/files/TwoSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="a rectangle in a square"><img src="/notes/files/ARectangleinaSquare_small.png" style="width: 10%"></a><a href="two half-squares and a circle"><img src="/notes/files/TwoHalfSquaresandaCircle_small.png" style="width: 10%"></a><a href="two circles and two semi-circles"><img src="/notes/files/TwoCirclesandTwoSemiCircles_small.png" style="width: 10%"></a><a href="two overlapping semi-circles"><img src="/notes/files/TwoOverlappingSemiCircles_small.png" style="width: 10%"></a><a href="nested semi-circles"><img src="/notes/files/NestedSemiCircles_small.png" style="width: 10%"></a><a href="two semi-circles inside a semi-circle"><img src="/notes/files/TwoSemiCirclesInsideaSemiCircle_small.png" style="width: 10%"></a><a href="rectangles in concentric rings"><img src="/notes/files/RectanglesinConcentricRings_small.png" style="width: 10%"></a><a href="three squares and a semi-circle"><img src="/notes/files/ThreeSquaresandaSemiCircle_small.png" style="width: 10%"></a><a href="two squares on a circle"><img src="/notes/files/TwoSquaresonaCircle_small.png" style="width: 10%"></a><a href="square in a semi-circle in a square"><img src="/notes/files/SquareinaSemiCircleinaSquare_small.png" style="width: 10%"></a><a href="arbelos"><img src="/notes/files/Arbelos_small.png" style="width: 10%"></a><a href="two quarter circles and a semi-circle ii"><img src="/notes/files/TwoQuarterCirclesandaSemiCircleII_small.png" style="width: 10%"></a><a href="three overlapping semi-circles"><img src="/notes/files/ThreeOverlappingSemiCircles_small.png" style="width: 10%"></a><a href="hexagon in a quarter circle"><img src="/notes/files/HexagoninaQuarterCircle_small.png" style="width: 10%"></a><a href="two squares in a semi-circle"><img src="/notes/files/TwoSquaresinaSemiCircle_small.png" style="width: 10%"></a><a href="seven quarter circles inside a semi-circle"><img src="/notes/files/SevenQuarterCirclesInsideaSemiCircle_small.png" style="width: 10%"></a><a href="two quarter circles in a semi-circle"><img src="/notes/files/TwoQuarterCirclesinaSemiCircle_small.png" style="width: 10%"></a><a href="semi-circle and quarter circle in a square"><img src="/notes/files/SemiCircleandQuarterCircleinaSquare_small.png" style="width: 10%"></a><a href="quarter circles in a rectangle in a circle"><img src="/notes/files/QuarterCirclesinaRectangleinaCircle_small.png" style="width: 10%"></a><a href="three circles"><img src="/notes/files/ThreeCircles_small.png" style="width: 10%"></a><a href="rectangle, circle, and triangle"><img src="/notes/files/RectangleCircleandTriangle_small.png" style="width: 10%"></a><a href="three triangles and a rectangle inside a circle"><img src="/notes/files/ThreeTrianglesandaRectangleInsideaCircle_small.png" style="width: 10%"></a><a href="triangle inside a square"><img src="/notes/files/TriangleInsideaSquare_small.png" style="width: 10%"></a><a href="semi-circle and tangents in a square"><img src="/notes/files/SemiCircleandTangentsinaSquare_small.png" style="width: 10%"></a><a href="triangle inside circle and triangle"><img src="/notes/files/TriangleInsideCircleandTriangle_small.png" style="width: 10%"></a><a href="two squares overlapping a semi-circle"><img src="/notes/files/TwoSquaresOverlappingaSemiCircle_small.png" style="width: 10%"></a><a href="circle in a trapezium"><img src="/notes/files/CircleinaTrapezium_small.png" style="width: 10%"></a><a href="semi-circle in a square ii"><img src="/notes/files/SemiCircleinaSquareII_small.png" style="width: 10%"></a><a href="a quarter circle and a semi-circle in a triangle"><img src="/notes/files/AQuarterCircleandaSemiCircleinaTriangle_small.jpeg" style="width: 10%"></a><a href="two triangles in a semi-circle"><img src="/notes/files/TwoTrianglesinaSemiCircle_small.png" style="width: 10%"></a><a href="zig-zag inside a rectangle"><img src="/notes/files/ZigzagInsideaRectangle_small.png" style="width: 10%"></a><a href="semi-circles in a rectangle"><img src="/notes/files/SemiCirclesinaRectangle_small.png" style="width: 10%"></a><a href="five rectangles in a semi-circle"><img src="/notes/files/FiveRectanglesinaSemiCircle_small.jpeg" style="width: 10%"></a><a href="two semi-circles in a semi-circle"><img src="/notes/files/TwoSemiCirclesinaSemiCircle_small.png" style="width: 10%"></a><a href="four squares in a circle"><img src="/notes/files/FourSquaresinaCircle_small.png" style="width: 10%"></a><a href="two semi-circles inside a semi-circle ii"><img src="/notes/files/TwoSemiCirclesInsideaSemiCircleII_small.png" style="width: 10%"></a><a href="two rectangles and a semi-circle"><img src="/notes/files/TwoRectanglesandaSemiCircle_small.png" style="width: 10%"></a><a href="two semi-circles in a square"><img src="/notes/files/TwoSemiCirclesinaSquare_small.png" style="width: 10%"></a><a href="a circle in a rectangle"><img src="/notes/files/ACircleinaRectangle_small.jpeg" style="width: 10%"></a>
## Trigonometry
* [[trigonometry]] 

   <a href="circles in rhombii sequel"><img src="/notes/files/CirclesinRhombiiSequal_small.png" style="width: 10%"></a><a href="angle formed by three squares"><img src="/notes/files/AngleFormedbyThreeSquares_small.png" style="width: 10%"></a>
* [[cosine rule]] 

* [[sine rule]] 

   <a href="four squares around a quadrilateral"><img src="/notes/files/FourSquaresAroundaQuadrilateral_small.png" style="width: 10%"></a>
* [[sine formula for the area of a triangle]] 

* [[compound angle formulae]] 

* Various Trigonometry

  <a href="a square in a square"><img src="/notes/files/ASquareinaSquare_small.jpeg" style="width: 10%"></a><a href="four congruent triangles"><img src="/notes/files/FourCongruentTriangles_small.jpeg" style="width: 10%"></a>
* With previous categories

  <a href="five circles in a square"><img src="/notes/files/FiveCirclesinaSquare_small.png" style="width: 10%"></a><a href="trisected hexagon"><img src="/notes/files/TrisectedHexagon_small.png" style="width: 10%"></a><a href="stacked triangles"><img src="/notes/files/StackedTriangles_small.png" style="width: 10%"></a><a href="a square and a triangle"><img src="/notes/files/ASquareandaTriangle_small.jpeg" style="width: 10%"></a><a href="two semi-circles and two quarter circles"><img src="/notes/files/TwoSemiCirclesandTwoQuarterCircles_small.jpeg" style="width: 10%"></a><a href="four rectangles and a hexagon"><img src="/notes/files/FourRectanglesandaHexagon_small.png" style="width: 10%"></a><a href="three triangles in a circle in a triangle"><img src="/notes/files/ThreeTrianglesinaCircleinaTriangle_small.png" style="width: 10%"></a>
## Algebra
* [[quadratics]] 

* [[quadratic equations]] 

* [[difference of two squares]] 

* With previous categories

  <a href="three squares in a circle ii"><img src="/notes/files/ThreeSquaresinaCircleII_small.png" style="width: 10%"></a><a href="similar rectangles"><img src="/notes/files/SimilarRectangles_small.png" style="width: 10%"></a><a href="two congruent rectangles in a square"><img src="/notes/files/TwoCongruentRectanglesinaSquare_small.png" style="width: 10%"></a><a href="subdivided hexagon iii"><img src="/notes/files/SubdividedHexagonIII_small.jpeg" style="width: 10%"></a>
## Other Techniques
* [[hidden line technique]] 

* [[invariance principle]] 

   <a href="four parallel semi-circles"><img src="/notes/files/FourParallelSemiCircles_small.png" style="width: 10%"></a><a href="four squares iv"><img src="/notes/files/FourSquaresIV_small.png" style="width: 10%"></a><a href="four squares"><img src="/notes/files/FourSquares_small.png" style="width: 10%"></a><a href="four squares v"><img src="/notes/files/FourSquaresV_small.png" style="width: 10%"></a><a href="regular hexagon and rectangle"><img src="/notes/files/RegularHexagonandRectangle_small.png" style="width: 10%"></a><a href="square in a triangle in a square"><img src="/notes/files/SquareinaTriangleinaSquare_small.png" style="width: 10%"></a><a href="three triangles in a hexagon"><img src="/notes/files/ThreeTrianglesinaHexagon_small.png" style="width: 10%"></a><a href="two triangles overlapping a quarter circle"><img src="/notes/files/TwoTrianglesOverlappingaQuarterCircle_small.png" style="width: 10%"></a><a href="two regular hexagons"><img src="/notes/files/TwoRegularHexagons_small.png" style="width: 10%"></a><a href="two quarter circles and a semi-circle"><img src="/notes/files/TwoQuarterCirclesandaSemiCircle_small.png" style="width: 10%"></a><a href="two overlapping squares iii"><img src="/notes/files/TwoOverlappingSquaresIII_small.png" style="width: 10%"></a><a href="two equilateral triangles ii"><img src="/notes/files/TwoEquilateralTrianglesII_small.jpeg" style="width: 10%"></a><a href="three quarter circles ii"><img src="/notes/files/ThreeQuarterCirclesII_small.jpeg" style="width: 10%"></a><a href="three squares and a rectangle"><img src="/notes/files/ThreeSquaresandaRectangle_small.jpeg" style="width: 10%"></a><a href="five regular polygons"><img src="/notes/files/FiveRegularPolygons_small.jpeg" style="width: 10%"></a><a href="three squares v"><img src="/notes/files/ThreeSquaresV_small.jpeg" style="width: 10%"></a><a href="two squares ii"><img src="/notes/files/TwoSquaresII_small.jpeg" style="width: 10%"></a><a href="two semi-circles and two quarter circles"><img src="/notes/files/TwoSemiCirclesandTwoQuarterCircles_small.jpeg" style="width: 10%"></a><a href="five equilateral triangles ii"><img src="/notes/files/FiveEquilateralTrianglesII_small.jpeg" style="width: 10%"></a><a href="two quarter circles and a circle"><img src="/notes/files/TwoQuarterCirclesandaCircle_small.jpeg" style="width: 10%"></a><a href="four quarter circles ii"><img src="/notes/files/FourQuarterCirclesII_small.png" style="width: 10%"></a><a href="three squares iv"><img src="/notes/files/ThreeSquaresIV_small.png" style="width: 10%"></a><a href="two equilateral triangles iii"><img src="/notes/files/TwoEquilateralTrianglesIII_small.jpeg" style="width: 10%"></a><a href="quarter circle overlapping a circle"><img src="/notes/files/QuarterCircleOverlappingaCircle_small.png" style="width: 10%"></a><a href="two overlapping triangles ii"><img src="/notes/files/TwoOverlappingTrianglesII_small.png" style="width: 10%"></a><a href="hexagon and a square"><img src="/notes/files/HexagonandaSquare_small.png" style="width: 10%"></a><a href="four squares in a semi-circle"><img src="/notes/files/FourSquaresinaSemiCircle_small.png" style="width: 10%"></a><a href="triangle in two tilted squares"><img src="/notes/files/TriangleinTwoTiltedSquares_small.png" style="width: 10%"></a><a href="five equilateral triangles"><img src="/notes/files/FiveEquilateralTriangles_small.png" style="width: 10%"></a><a href="five semi-circles"><img src="/notes/files/FiveSemiCircles_small.png" style="width: 10%"></a><a href="four squares vii"><img src="/notes/files/FourSquaresVII_small.png" style="width: 10%"></a><a href="two squares on a hexagon"><img src="/notes/files/TwoSquaresonaHexagon_small.png" style="width: 10%"></a><a href="multiple semi-circles iii"><img src="/notes/files/MultipleSemiCirclesIII_small.png" style="width: 10%"></a><a href="two overlapping triangles"><img src="/notes/files/TwoOverlappingTriangles_small.png" style="width: 10%"></a><a href="four squares inside a rectangle"><img src="/notes/files/FourSquaresInsideaRectangle_small.png" style="width: 10%"></a><a href="triangle in a rectangle"><img src="/notes/files/TriangleinaRectangle_small.png" style="width: 10%"></a><a href="square overlapping a square and a rectangle"><img src="/notes/files/SquareOverlappingaSquareandaRectangle_small.png" style="width: 10%"></a><a href="chord splitting a square in half"><img src="/notes/files/ChordSplittingaSquareinHalf_small.png" style="width: 10%"></a><a href="rectangle tilted over a square"><img src="/notes/files/RectangleTiltedOveraSquare_small.png" style="width: 10%"></a><a href="two semi-circles in a circle"><img src="/notes/files/TwoSemiCirclesinaCircle_small.png" style="width: 10%"></a><a href="four squares iii"><img src="/notes/files/FourSquaresIII_small.png" style="width: 10%"></a><a href="a rectangle in a square"><img src="/notes/files/ARectangleinaSquare_small.png" style="width: 10%"></a><a href="two half-squares and a circle"><img src="/notes/files/TwoHalfSquaresandaCircle_small.png" style="width: 10%"></a><a href="two overlapping triangles and a circle"><img src="/notes/files/TwoOverlappingTrianglesandaCircle_small.png" style="width: 10%"></a><a href="two tilted squares"><img src="/notes/files/TwoTiltedSquares_small.png" style="width: 10%"></a><a href="two circles inside an equilateral triangle"><img src="/notes/files/TwoCirclesInsideanEquilateralTriangle_small.png" style="width: 10%"></a><a href="three overlapping rectangles ii"><img src="/notes/files/ThreeOverlappingRectanglesII_small.png" style="width: 10%"></a><a href="two semi-circles diagonally across a square"><img src="/notes/files/TwoSemiCirclesDiagonallyAcrossaSquare_small.png" style="width: 10%"></a><a href="quadrilateral splitting a semi-circle"><img src="/notes/files/QuadrilateralSplittingaSemiCircle_small.png" style="width: 10%"></a><a href="two pentagons"><img src="/notes/files/TwoPentagons_small.png" style="width: 10%"></a><a href="angles in two hexagons"><img src="/notes/files/AnglesinTwoHexagons_small.png" style="width: 10%"></a><a href="three overlapping squares"><img src="/notes/files/ThreeOverlappingSquares_small.png" style="width: 10%"></a><a href="two squares in a semi-circle"><img src="/notes/files/TwoSquaresinaSemiCircle_small.png" style="width: 10%"></a><a href="three regular hexagons iii"><img src="/notes/files/ThreeRegularHexagonsIII_small.png" style="width: 10%"></a><a href="stacked triangles"><img src="/notes/files/StackedTriangles_small.png" style="width: 10%"></a><a href="angle formed by two squares ii"><img src="/notes/files/AngleFormedbyTwoSquaresII_small.png" style="width: 10%"></a><a href="three hexagons in a trapezium"><img src="/notes/files/ThreeHexagonsinaTrapezium_small.png" style="width: 10%"></a><a href="two regular hexagons ii"><img src="/notes/files/TwoRegularHexagonsII_small.png" style="width: 10%"></a><a href="rectangle on a hexagon"><img src="/notes/files/RectangleonaHexagon_small.png" style="width: 10%"></a>
* With previous categories

  <a href="three squares iii"><img src="/notes/files/ThreeSquaresIII_small.png" style="width: 10%"></a><a href="two squares and a quarter circle"><img src="/notes/files/TwoSquaresandaQuarterCircle_small.jpeg" style="width: 10%"></a><a href="three regular hexagons ii"><img src="/notes/files/ThreeRegularHexagonsII_small.png" style="width: 10%"></a><a href="four congruent squares inside a larger square"><img src="/notes/files/FourCongruentSquaresInsideaLargerSquare_small.png" style="width: 10%"></a><a href="six squares and a quarter circle"><img src="/notes/files/SixSquaresandaQuarterCircle_small.png" style="width: 10%"></a>