Question 40
The quadrilateral $ABCD$ is inscribed in a circle. The point $P$ lies in the interior of $ABCD$, and $\angle PAB = \angle PBC = \angle PCD = \angle PDA$. The lines $AD$ and $BC$ meet at $Q$, and the lines $AB$ and $CD$ meet at $R$. Prove that the lines $PQ$ and $PR$ form the same angle as the diagonals of $ABCD$.
Supplemental illustration (AI-generated; gray vertices, if present, have unspecified colors):
Supplemental illustration (AI-generated; gray vertices, if present, have unspecified colors):