MathNet 2017-part-01 — 176 problems (EN–VI) Question 18

In the isosceles triangle $ABC$ with $\overline{AC} = \overline{BC}$ we denote by $D$ the foot of the altitude through $C$. The midpoint of $CD$ is denoted by $M$. The line $BM$ intersects $AC$ in $E$. Prove that the length of $AC$ is three times that of $CE$.


Figure 4: Problem 16