Problem

Source: Polish MO

Tags: geometry



In an acute triangle $ABC$ the bisector of $\angle BAC$ crosses $BC$ at $D$. Points $P$ and $Q$ are orthogonal projections of $D$ on lines $AB$ and $AC$. Prove that $[APQ]=[BCQP]$ if and only if the circumcenter of $ABC$ lies on $PQ$.