Question 48
Let $ABC$ be a triangle and $\Gamma$ the circle with diameter $AB$. The bisectors of $\angle BAC$ and $\angle ABC$ intersect $\Gamma$ (also) at $D$ and $E$, respectively. The incircle of $ABC$ meets $BC$ and $AC$ at $F$ and $G$, respectively. Prove that $D, E, F$ and $G$ are collinear.