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equal angles, tangents of circumcircle (2020 Novosibirsk Oral Geo Oly 9.6)

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May 24, 2021
geometryequal anglesTangents

Problem Statement

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