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parallel lines, taking the symmetrics of orthocenter wrt to sides

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P7

August 2, 2018
geometrysymmetryorthocenter

Problem Statement

The altitudes AA1AA_1 and CC1CC_1 of a triangle ABCABC meet at point HH. Point HAH_A is symmetric to HH about AA. Line HAC1H_AC_1 meets BCBC at point C′C' , point A′A' is defined similarly. Prove that A′C′//ACA' C' // AC.
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