TUYMAADA 2017 J5

$BL$ is the bisector of an isosceles triangle $ABC$ . A point $D$ is chosen on the Base $BC$ and a point $E$ is chosen on the lateral side $AB$ so that $AE=\frac {1}{2}AL=CD$ . Prove that $LE=LD$ .

Tuymaada 2017 Q5 Juniors