Question 66
Let $ABCD$ be a parallelogram and let $G$ be the centroid of triangle $ABD$. Let $P$ and $Q$ be the points of line $(BD)$ such that lines $(GP)$ and $(PC)$ are perpendicular and lines $(GQ)$ and $(QC)$ are perpendicular.
Prove that line $(AG)$ is the bisector of angle $\widehat{PAQ}$.
Prove that line $(AG)$ is the bisector of angle $\widehat{PAQ}$.