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Constant chord implies constant angle

Source: Canadian Mathematical Olympiad - 1986 - Problem 3.

July 3, 2011
geometry proposedgeometry

Problem Statement

A chord STST of constant length slides around a semicircle with diameter ABAB. MM is the midpoint of STST and PP is the foot of the perpendicular from SS to ABAB. Prove that ∠SPM\angle SPM is constant for all positions of STST.
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