RU-ALLRUSSIAN 2016 Problem 108

In acute triangle $ABC$ , $AC<BC$ , $M$ is midpoint of $AB$ and $\Omega$ is it's circumcircle.Let $C^\prime$ be antipode of $C$ in $\Omega$ . $AC^\prime$ and $BC^\prime$ intersect with $CM$ at $K,L$ ,respectively.The perpendicular drawn from $K$ to $AC^\prime$ and perpendicular drawn from $L$ to $BC^\prime$ intersect with $AB$ and each other and form a triangle $\Delta$ .Prove that circumcircles of $\Delta$ and $\Omega$ are tangent.(M.Kungozhin)