Question 79
Let $ABC$ be a scalene triangle with median $AM$. Let $K$ be the point of tangency of the incircle of triangle $ABC$ with the side $BC$. Prove that if the length of the side $BC$ is the arithmetic mean of the lengths of the sides $AB$ and $AC$ then the bisector of the angle $BAC$ passes through the midpoint of the line segment $KM$.