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right triangle and excircle given, collinear wanted

Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p4

July 30, 2019
geometryright triangleexcirclecollinear

Problem Statement

Let MM and NN be the midpoints of the hypotenuse ABAB and the leg BCBC of a right triangles ABCABC respectively. The excircle of the triangle ACMACM touches the side AMAM at point QQ, and line ACAC at point PP. Prove that points P,QP, Q and NN lie on one straight line.
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