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Iran geometry

Source: Iranian 3rd round 2016 first geometry exam problem 3

August 14, 2016
geometry

Problem Statement

Let ABCABC be a triangle and let AD,BE,CFAD,BE,CF be its altitudes . FA1,DB1,EC1FA_{1},DB_{1},EC_{1} are perpendicular segments to BC,AC,ABBC,AC,AB respectively. Prove that : ABCABC~A1B1C1A_{1}B_{1}C_{1}
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