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Parallel to Euler line

Source: Iranian National Olympiad (3rd Round) 2008

September 12, 2008
Eulergeometrygeometric transformationreflectiongeometry proposed

Problem Statement

Let la,lb,lc l_a,l_b,l_c be three parallel lines passing through A,B,C A,B,C respectively. Let la′ l_a' be reflection of la l_a into BC BC. lb′ l_b' and lc′ l_c' are defined similarly. Prove that la′,lb′,lc′ l_a',l_b',l_c' are concurrent if and only if la l_a is parallel to Euler line of triangle ABC ABC.
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