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CH is parallel to AB

Source: Baltic Way 2011

November 6, 2011
geometrycircumcirclegeometry proposed

Problem Statement

The incircle of a triangle ABCABC touches the sides BC,CA,ABBC,CA,AB at D,E,FD,E,F, respectively. Let GG be a point on the incircle such that FGFG is a diameter. The lines EGEG and FDFD intersect at HH. Prove that CH∥ABCH\parallel AB.
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