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Romanian District Olympiad 2015, Grade VI, Problem 2

Source:

September 25, 2018
geometryperpendicular bisectorromania

Problem Statement

Let ABC ABC be an obtuse triangle with AB=AC,M AB=AC, M the symmetric point of A A with respect to C, C, and P P the intersection of the line AB AB with the perpendicular bisector of the segment AB‾. \overline{AB} . Knowing that PM PM is perpendicular to BC, BC, show that APM APM is equilateral.
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