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isosceles wanted, semicircle related Puerto Rico TST 2023.1.2

Source:

March 23, 2024
geometryisoscelessemicircle

Problem Statement

Consider a semicircle with center MM and diameter ABAB. Let PP be a point in the semicircle, different from AA and BB, and let QQ be the midpoint of the arc APAP. The line parallel to QPQP through MM intersects PBPB at the point SS. Prove that the triangle PMSPMS is isosceles.
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