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Concurrency of lines involving altitudes

Source: Moldova TST Problem 7

April 1, 2015
geometry

Problem Statement

Consider an acute triangle ABCABC, points E,FE,F are the feet of the perpendiculars from BB and CC in △ABC\triangle ABC. Points II and JJ are the projections of points F,EF,E on the line BCBC, points K,LK,L are on sides AB,ACAB,AC respectively such that IK∥ACIK \parallel AC and JL∥ABJL \parallel AB. Prove that the lines IEIE,JFJF,KLKL are concurrent.
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