MathNet 2010 — Part 04 Question 104

The incircle of triangle $ABC$ touches $BC,CA$ at $D,E$, respectively. Line $DE$ meets the bisectors of $\angle ABC,\angle BAC$ at $F,G$, respectively. Let $S,T$ be the perpendicular projections of $A,B$ onto $DE$. Prove that $SF=GT$.