RU-ALLRUSSIAN 2016 Problem 118

Medians $AM_A,BM_B,CM_C$ of triangle $ABC$ intersect at $M$ .Let $\Omega_A$ be circumcircle of triangle passes through midpoint of $AM$ and tangent to $BC$ at $M_A$ .Define $\Omega_B$ and $\Omega_C$ analogusly.Prove that $\Omega_A,\Omega_B$ and $\Omega_C$ intersect at one point.(A.Yakubov)