Problem

The diagram shows a circle with centre $A$ and radius $r$ passing through points $B$, $C$ and $D$. A larger circle of radius $s$ has centre $C$ and passes through $B$ and $D$. The length $BD$ is also $s$.

(a) Show that $s=\sqrt{3}r$.

(b) Find an expression for the area of the shaded region. Give your answer in the form $(a+b\pi)r^2$, where $a$ and $b$ are constants to be found.