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Lines are parallel

Source: Sharygin Geometry Olympiad Correspondence round 2016 P-3 Grade 8

February 20, 2017
geometry

Problem Statement

Let AH1AH_1, BH2BH_2 be two altitudes of an acute-angled triangle ABCABC , DD be the projection of H1H_1 to ACAC, EE be the projection of DD to ABAB, FF be the common point of EDED and AH1AH_1. Prove that H2F∥BCH_2F \parallel BC.
(Proposed by E.Diomidov)
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