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angles wanted in right triangle, reflection (2021 Auckland MO S2)

Source:

October 30, 2021
geometrygeometric transformationreflection

Problem Statement

Triangle ABCABC is the right angled triangle with the vertex CC at the right angle. Let PP be the point of reflection of CC about ABAB. It is known that PP and two midpoints of two sides of ABCABC lie on a line. Find the angles of the triangle.
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