2.3: Right-angled triangle with two circular sectors

The diagram shows a right-angled triangle $ABC$ with $AB = 8\text{ cm}$ and angle $ABC = \tfrac{\pi}{2}$ radians. The points $D$ and $E$ lie on $AC$ and $BC$ respectively. $BAD$ and $ECD$ are sectors of the circles with centres $A$ and $C$ respectively. Angle $BAD = \tfrac{2\pi}{9}$ radians.