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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.

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

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