MathDB
Equality of perimeters

Source: VII Centroamerican and Caribbean Olympiad 2005, Problem 5

July 29, 2005
geometryperimetertrigonometryparallelogramangle bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle, HH the orthocenter and MM the midpoint of ACAC. Let ℓ\ell be the parallel through MM to the bisector of ∠AHC\angle AHC. Prove that ℓ\ell divides the triangle in two parts of equal perimeters. Pedro Marrone, Panamá
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