MathNet 2019-part-05 — 184 problems (EN–VI) Question 158

Let $ABC$ be a triangle. A point $D$ is chosen on the external angle bisector of angle $ABC$ lying inside the angle $ABC$. Assume that $\angle BCD = 60^\circ$ and $CD = 2AB$. Let $M$ be the midpoint of $BD$. Prove that the triangle $AMC$ is isosceles.
(A. Kuznetsov)