IGO 2022 A1

Four points $A$ , $B$ , $C$ and $D$ lie on a circle $\omega$ such that $AB=BC=CD$ . The tangent line to $\omega$ at point $C$ intersects the tangent line to $\omega$ at $A$ and the line $AD$ at $K$ and $L$ . The circle $\omega$ and the circumcircle of triangle $KLA$ intersect again at $M$ . Prove that $MA=ML$ .

Proposed by Mahdi Etesamifard