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Source: Brazilian Mathematical Olympiad 2024, Level 2, Problem 6

October 12, 2024
geometryparallelisoscelesexcirclemidpoint

Problem Statement

Let ABCABC be an isosceles triangle with AB=BCAB = BC. Let DD be a point on segment ABAB, EE be a point on segment BCBC, and PP be a point on segment DEDE such that AD=DPAD = DP and CE=PECE = PE. Let MM be the midpoint of DEDE. The line parallel to ABAB through MM intersects ACAC at XX and the line parallel to BCBC through MM intersects ACAC at YY. The lines DXDX and EYEY intersect at FF. Prove that FPFP is perpendicular to DEDE.
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