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AMPN is inscriptable implies ABC is isosceles

Source: IberoAmerican 1987 Q2

November 12, 2010
geometrygeometric transformationreflectionconicshyperbolasymmetrytrigonometry

Problem Statement

In a triangle ABCABC, MM and NN are the respective midpoints of the sides ACAC and ABAB, and PP is the point of intersection of BMBM and CNCN. Prove that, if it is possible to inscribe a circle in the quadrilateral AMPNAMPN, then the triangle ABCABC is isosceles.
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