Question 140
Let $D$ and $E$ be the midpoints of sides $BC$ and $CA$ of the triangle $ABC$ respectively. The lines $AD$ and $BE$ intersect the circumcircle of the triangle $ABC$ additionally in points $P$ and $Q$ respectively. Suppose that $|DP| = |EQ|$. Prove that the triangle $ABC$ is isosceles with apex $C$.