Question 42
The points $M$ and $N$ are the tangent points of the sides $[AB]$ and $[AC]$ of the triangle $ABC$ to the incircle with the center $I$. The internal bissectrices, drawn from the vertices $B$ and $C$, intersect the straight line $MN$ at points $P$ and $Q$ respectively. If $F$ is the intersection point of the straight lines $CP$ and $BQ$, then prove that the straight lines $FI$ and $BC$ are perpendicular.