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bisector of <BEA _|_ MR

Source: Mathematics Regional Olympiad of Mexico West 2021 P5

September 9, 2022
perpendiculargeometry

Problem Statement

Let ABCABC be a triangle such that ACAC is its shortest side. A point PP is inside it and satisfies that BP=ACBP = AC. Let RR be the midpoint of BCBC and let MM be the midpoint of APAP. Let EE be the intersection of BPBP and ACAC. Prove that the bisector of angle ∠BEA\angle BE A is perpendicular to segment MRMR.
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