Question 73
In a triangle $ABC$, $|AB| = |AC|$, $D$ is the midpoint of $[BC]$ and $E$ is the foot of the perpendicular from $D$ to the line $AC$. Let $F$ be the second point where the line $BE$ intersects the circumcircle of the triangle $ABD$. If $G$ is the intersection point of the lines $DE$ and $AF$, then show that $|DG| = |GE|$.
