# Solution to the Two Squares on a Triangle Puzzle +-- {.image} [[TwoSquaresonaTriangle.png:pic]] > Two squares sit on the hypotenuse of a right-angled triangle. What's the angle? =-- ## Solution by [[Angle in a Semi-Circle]], [[Angle at the Circumference is Half the Angle at the Centre]] +-- {.image} [[TwoSquaresonaTriangleLabelled.png:pic]] =-- With the points labelled as above, point $O$ is the [[midpoint]] of $B D$ so the circle centred on $O$ which passes through $B$ also passes through $A$ and $D$. Since the [[angle in a semi-circle]] is $90^\circ$ and angle $D \hat{C} B$ is $90^\circ$, the circle also passes through $C$. Then angle $A \hat{O} B$ is $90^\circ$ so since the [[angle at the circumference is half the angle at the centre]], angle $A \hat{C} B$ is $45^\circ$.