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Intersection of a cevian with the incircle

Source: South African MO 2005 Q4

May 27, 2012
geometryanalytic geometrypower of a pointgeometry unsolved

Problem Statement

The inscribed circle of triangle ABCABC touches the sides BCBC, CACA and ABAB at DD, EE and FF respectively. Let QQ denote the other point of intersection of ADAD and the inscribed circle. Prove that EQEQ extended passes through the midpoint of AFAF if and only if AC=BCAC = BC.
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