CMO 2014 Problem 4

The quadrilateral $A B C D$ is inscribed in a circle. The point $P$ lies in the interior of $A B C D$, and $\angle P A B=\angle P B C=\angle P C D=\angle P D A$. The lines $A D$ and $B C$ meet at $Q$, and the lines $A B$ and $C D$ meet at $R$. Prove that the lines $P Q$ and $P R$ form the same angle as the diagonals of $A B C D$.