MathNet 2017-part-01 — 176 problems (EN–VI) Question 6

In the isosceles triangle $ABC$ with $\overline{AC} = \overline{BC}$, let $D$ be the foot of the altitude through $C$ and let $M$ be the midpoint of the segment $CD$. The line $BM$ intersects $AC$ at $E$. Prove that $AC$ is three times as long as $CE$.
(Erich Windischbacher)