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Circumcircles intersect at one point

Source: All russian olympiad 2016,Day2,grade 11,P8

May 1, 2016
geometrycircumcirclegeometry proposedmedian

Problem Statement

Medians AMA,BMB,CMCAM_A,BM_B,CM_C of triangle ABCABC intersect at MM.Let ΩA\Omega_A be circumcircle of triangle passes through midpoint of AMAM and tangent to BCBC at MAM_A.Define ΩB\Omega_B and ΩC\Omega_C analogusly.Prove that ΩA,ΩB\Omega_A,\Omega_B and ΩC\Omega_C intersect at one point.(A.Yakubov) [hide=P.S]sorry for my mistake in translation :blush: :whistling: .thank you jred for your help :coolspeak:
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