MathNet 2016-part-01 — 184 problems (EN–VI) Question 176

Let $D$ be an arbitrary point on the base $AB$ of an isosceles triangle $ABC$. Let $E$ be such that $ADEC$ is a parallelogram. The point $F$ on the ray opposite to $ED$ satisfies $EF = EB$. Prove that the length of the chord cut by the line $BE$ in the circumcircle of triangle $ABF$ is twice the length of $AC$.
(Jan Kuchařík, Patrik Bak)