On sides AB and AC of an acute triangle ΔABC, with orthocenter H and circumcenter O, are given points P and Q respectively such that APHQ is a parallelogram. Prove the following equality:
\begin{align*}
\frac{PB\cdot PQ}{QA\cdot QO}=2
\end{align*} geometryorthocenterparallelogramCircumcentercircumcircle