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A righ-angled isosceles triangle

Source: Baltic Way 2000 Problem 2

February 13, 2009
trigonometrygeometry unsolvedgeometry

Problem Statement

Given an isosceles triangle ABC ABC with \angle A \equal{} 90^{\circ}. Let M M be the midpoint of AB AB. The line passing through A A and perpendicular to CM CM intersects the side BC BC at P P. Prove that \angle AMC \equal{} \angle BMP.
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