# Prove a figure is a cyclic quadrilateral

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.

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