Difficult Geometry Problem

Let ABCD be a cyclic quadrilateral. Let P be the intersection of $\overleftrightarrow{AD}$ and $\overleftrightarrow{BC}$, and let Q be the intersection of $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$. Prove that the angle bisectors of angle DPC and angle AQD are perpendicular.

Thanks so much!