Question 143
In a non-isosceles triangle $ABC$, $I$ is the centre of the incircle. The bisector of $\angle BAC$ meets the circumcircle of $\triangle ABC$ again at $D$. The line through $I$ perpendicular to $AD$ meets $BC$ at $F$. The midpoint of the arc $BC$ on which $A$ lies is called $M$. The line $MI$ meets the circle through $B, I$ and $C$ again at $N$. Prove that $FN$ is tangent to the circle through $B, I$ and $C$.
