# Solution to the Three Triangles and a Rectangle Inside a Circle Puzzle +-- {.image} [[ThreeTrianglesandaRectangleInsideaCircle.png:pic]] > Three equilateral triangles and a rectangle are stacked up inside this circle. What's the angle? =-- ## Solution by [[Symmetry]] and [[Angle in a Semi-Circle]] +-- {.image} [[ThreeTrianglesandaRectInaCircleLabelled.png:pic]] =-- In the diagram above, the vertical line through the [[midpoint]] of [[chord]] $B C$ passes through the centre of the circle. It is therefore a [[line of symmetry]] of both the circle and the central [[equilateral triangle]]. Since the points $A$ and $D$ depend on the circle and the central equilateral triangle, reflecting in the vertical line swaps $A$ and $D$ and so in particular the line joining $A$ to $D$ is the continuation of their horizontal sides. This establishes angle $D \hat{A} E$ as a right-angle, and so $E A$ is a diameter of the circle since the [[angle in a semi-circle]] is a right-angle. By the same result, angle $E \hat{D} F$ is then also a right-angle.