CGMO 2022 Problem 5

Two points $K$ and $L$ are chosen inside triangle $ABC$ and a point $D$ is chosen on the side $AB$ . Suppose that $B$ , $K$ , $L$ , $C$ are concyclic, $\angle AKD = \angle BCK$ and $\angle ALD = \angle BCL$ . Prove that $AK = AL$ .