Question 11
In the acute triangle $ABC$, the bisectors of $\angle A$, $\angle B$ and $\angle C$ intersect the circumcircle again in $A_{1}$, $B_{1}$ and $C_{1}$, respectively. Let $M$ be the point of intersection of $AB$ and $B_{1}C_{1}$, and let $N$ be the point of intersection of $BC$ and $A_{1}B_{1}$. Prove that $MN$ passes through the incentre of triangle $ABC$.