MathDB

6

Part of 2011 South africa National Olympiad

Problems(1)

Regarding the incircle and Gergonne Point

Source: SAMO 2011 Senior Round 3 Problem 6

9/7/2011
In triangle ABCABC, the incircle touches BCBC in DD, CACA in EE and ABAB in FF. The bisector of ∠BAC\angle BAC intersects BCBC in GG. The lines BEBE and CFCF intersect in JJ. The line through JJ perpendicular to EFEF intersects BCBC in KK. Prove that
GKDK=AECE+AFBF\frac{GK}{DK}=\frac{AE}{CE}+\frac{AF}{BF}
geometrysymmetrygeometry unsolved