MathNet 2024-part-03 — 168 problems (EN–VI) Question 143

Let $ABC$ be a triangle such that $\angle ACB = 90^\circ$ and $\angle BAC = 36^\circ$. Let $AL$ be the angle bisector of the angle $\angle BAC$. The point $M$ is taken on $AL$ so that $AM = MB$. Prove that $AM = 2 CL$.