Question 184
Let $D$ and $E$ be the midpoints of the sides $BC$ and $CA$ of the triangle $ABC$, respectively. The lines $AD$ and $BE$ intersect the circumcircle of the triangle $ABC$ again in the points $P$ and $Q$, respectively. Suppose that $|DP|=|EQ|$. Prove that the triangle $ABC$ is isosceles with apex $C$.
