MathDB
point on median, projection to sides and perpendiculars

Source: Bulgaria 1987 P5

June 15, 2021
geometryTriangles

Problem Statement

Let EE be a point on the median ADAD of a triangle ABCABC, and FF be the projection of EE onto BCBC. From a point MM on EFEF the perpendiculars MNMN to ACAC and MPMP to ABAB are drawn. Prove that if the points N,E,PN,E,P lie on a line, then MM lies on the bisector of ∠BAC\angle BAC.
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