# Two Rectangles in a Semi-Circle +-- {.image} [[TwoRectanglesinaSemiCircle.png:pic]] > Two congruent rectangles sitting in a semicircle. What's the angle? =-- ## Solution by [[Properties of Chords]] and [[Angle at the Circumference is Half the Angle at the Centre]] +-- {.image} [[TwoRectanglesinaSemiCirclePuzzle.png:pic]] =-- As the rectangles are [[congruent]], the diagonals $O A$ and $O B$ are of equal length and so triangle $A O B$ is [[isosceles]]. This means that point $O$ lies on the [[perpendicular bisector]] of $A B$. Since $A B$ is a [[chord]], the centre of the circle also lies on that perpendicular bisector. Since $O$ is also on the diameter, then, it is the centre. Using the fact that the [[angle at the circumference is half the angle at the centre]], angle $A \hat{C} B$ is half of angle $A \hat{O} B$, read anti-clockwise from $A$ to $B$. As the rectangles are congruent, angles $A \hat{O} D$ and $D \hat{O} B$ add up to $90^\circ$, so angle $A \hat{O} B$ is $270^\circ$, and hence angle $A \hat{C} B$ is $135^\circ$.