Question 143
A circle, inscribed into a triangle $ABC$, touches its sides $AB$, $BC$ and $CA$ in the points $N$, $P$, $K$ respectively. A segment $BK$ intersects the inscribed circle the second time in a point $L$.
Let us define points $T = AL \cap NK$, $Q = CL \cap KP$. Prove that straight lines $BK$, $NQ$ and $PT$ intersect in one single point.
Let us define points $T = AL \cap NK$, $Q = CL \cap KP$. Prove that straight lines $BK$, $NQ$ and $PT$ intersect in one single point.