Question 17
Let $I$ be the incentre of triangle $ABC$. A line through $I$ meets the interior of segment $AB$ at $M$ and the interior of segment $BC$ at $N$. Assume that $BMN$ is an acute triangle. Let $K,L$ be points on segment $AC$ such that $\angle BMI=\angle ILA$ and $\angle BNI=\angle IKC$. Prove that $|AM|+|KL|+|CN|=|AC|$.