Question 34
Let $ABC$ be an acute-angled and scalene triangle. Consider the altitudes $BE$ and $CD$, that intersect in $H$. The bisector of the angle $B\hat{A}C$ intersects the altitudes $BE$ and $CD$ in $P$ and $Q$ respectively. Let $T$ be the orthocenter of the triangle $HPQ$. Prove that the triangles $TDA$ and $TEA$ have the same area.