Prove a figure is a cyclic quadrilateral

Question

In the figure below, $O$ is the center of the circle. If angle CPB is $90^\circ$, then prove that $AOEF$ is a cyclic quadrilateral.

Answer 1

Connect $OB$. $\angle AOP=\angle POB$ and $\angle AOP+\angle POB=2\angle AFE$ implies $\angle AOP=\angle AFE$ and therefore $AOEF$ cocyclic.