Question 69
A tangent is drawn at $A$ to a circle centre $O$. Point $D$ is on this tangent and $B$, $C$ are on the circle such that $B$, $C$ and $D$ are collinear. Points $P$ and $Q$ are the circumcentres of triangles $ACD$ and $ABD$, respectively.
Prove $\angle AOB = \angle APD = \angle BQD$.
Prove $\angle AOB = \angle APD = \angle BQD$.