Question 83
$AD$ is a bisector of the triangle $ABC$. Line $AD$ intersects a second time the circumcircle of $\triangle ABC$ at point $E$. Let $K, L, M$ and $N$ be the midpoints of the segments $AB, BD, CD$ and $AC$ respectively, $P$ be the circumcenter of the triangle $EKL$, $Q$ be the circumcenter of the triangle $EMN$. Prove that $\angle PEQ = \angle BAC$.