Question 34
Let $ABC$ be a triangle with altitude $CH$, where $H$ is an interior point of the side $AB$. Denote by $P$ and $Q$ the incenters of $\triangle AHC$ and $\triangle BHC$, respectively. Prove that the quadrilateral $ABQP$ is cyclic if and only if either $AC = BC$ or $\angle ACB = 90^\circ$.