Question 31
Let $ADE$ an isosceles triangle in $A$. either the circle $\omega$, tangent to the lines $(AD)$ and $(AE)$ in $D$ and $E$. Let $B$ and $C$ two points beyond $D$ and $E$ on the lines $(AD)$ and $(AE)$. It is assumed that $BC \gt BD + CE$. Finally, either $F$ and $G$ two points on the segment $[BC]$ so that $BD = BF$ and $CG = CE$, the lines $(DG)$ and $(FE)$ intersect in $K$, the tangent to $\omega$ parallel to $(BC)$ and between $A$ and $(BC)$ key $\omega$ in $L$. Show that the center of the inscribed circle of $ABC$ is on $(KL)$.
