# Solution to the [[Angle in Two Overlapping Squares]] Puzzle +-- {.image} [[AngleinTwoOverlappingSquares.png:pic]] > These squares are the same size. What's the angle? =-- ## Solution by [[Angle at the Circumference is Half that at the Centre]] +-- {.image} [[AngleinTwoOverlappingSquaresAnnotated.png:pic]] =-- In the diagram above, the circle has centre $O$ and passes through point $A$. As the $O B$ is another side of the square, $O B$ has the same length as $O A$ and so the circle also passes through $B$. The squares are the same size, so $O C$ is also the same length and so the circle passes through $C$. Angle $A \hat{C} B$ is formed by joining a point on the circumference of the circle, $C$, to two other points, $A$ and $B$, and so since the [[angle at the circumference is half that at the centre]], it is half the angle formed by joining $A$ and $B$ to the centre, $O$. This angle is the corner of the [[square]] and so is a right-angle. Hence angle $A \hat{C} B = 45^\circ$.