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AM_|_MD if BC = 2 AC, AD = 2BD, BM=//MC

Source: 2023 Czech-Polish-Slovak Match Junior, individual p1 CPSJ

May 5, 2024
perpendiculargeometry

Problem Statement

Given a triangle ABCABC, BC=2⋅ACBC = 2 \cdot AC. Point MM is the midpoint of side BC BC and point DD lies on ABAB, with AD=2⋅BDAD = 2 \cdot BD. Prove that the lines AMAM and MDMD are perpendicular.
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