Question 21
In a circle $\omega$ centred at $O$, $AA^{\prime}$ and $BB^{\prime}$ are diameters perpendicular to each other such that the points $A,B,A^{\prime},B^{\prime}$ are arranged in an anticlockwise sense in this order. Let $P$ be a point on the minor arc $A^{\prime} B^{\prime}$ such that $AP$ intersects $BB^{\prime}$ at $D$ and $BP$ intersects $AA^{\prime}$ at $C$. Suppose the area of the quadrilateral $ABCD$ is $100$. Find the radius of $\omega$.