Question 191
Let $ABC$ a sharp triangle, $AB \lt AC$, and be $\Gamma$ its circumscribed circle. The tangent of $\Gamma$ in $A$ intersects the right $BC$ in $K$. The $\Omega$ circle, $KA$ and $K$ center, intersects the second time $\Gamma$ in $L$. The Circle $\Omega$ intersects the second right $BL$ in $M$ and right $CM$ in $N$. Show that the right $AN$ passes through the middle of the $BC$ segment.