Question 166
Let $P$ be the midpoint of the side $AB$ of the triangle $ABC$. The mirror image of the ray $PC$ by reflection across the line $AB$ intersects the circumcircle of the triangle $ABC$ in the point $D$. Let $E$ be the other intersection of the line $CP$ with the circumcircle of the triangle $ABC$. Prove that $|AE| = |BD|$.