Question 12
(IRE 1) Let $ABC$ be a triangle and $L$ the line through $C$ parallel to the side $AB$. Let the internal bisector of the angle at $A$ meet the side $BC$ at $D$ and the line $L$ at $E$ and let the internal bisector of the angle at $B$ meet the side $AC$ at $F$ and the line $L$ at $G$. If $GF=DE$, prove that $AC=BC$.