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equal angles wanted, circumcircle, tangents, midpoints given

Source: Oral Moscow Geometry Olympiad 2015 grades 10-11 p4

August 6, 2019
geometrycircumcircleequal anglesTangentsmidpoints

Problem Statement

In triangle ABCABC, point MM is the midpoint of BC,PBC, P is the intersection point of the tangents at points BB and CC of the circumscribed circle, NN is the midpoint of the segment MPMP. The segment ANAN intersects the circumscribed circle at point QQ. Prove that ∠PMQ=∠MAQ\angle PMQ = \angle MAQ.
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