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concurrent related to tangents to Euler circle and circumcircle

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P22

April 7, 2019
geometryNine Point CircleTangentscircumcircleconcurrencyconcurrent

Problem Statement

Let CX,CYCX, CY be the tangents from vertex CC of triangle ABCABC to the circle passing through the midpoints of its sides. Prove that lines XY,ABXY , AB and the tangent to the circumcircle of ABCABC at point CC concur.
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