SHARYGIN 2018 Problem 3

Let $AL$ be a bisector of triangle $ABC$ , $D$ be its midpoint, and $E$ be the projection of $D$ to $AB$ . It is known that $AC = 3AE$ . Prove that $CEL$ is an isosceles triangle.

Official text Sharygin Geometry Olympiad 2018 official paper, page 2. Quoted with source.

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