MathDB

4

Part of 2005 South africa National Olympiad

Problems(1)

Intersection of a cevian with the incircle

Source: South African MO 2005 Q4

5/27/2012
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.
geometryanalytic geometrypower of a pointgeometry unsolved