Question 28
In the triangle $ABC$, the points $M$ and $N$ lay onto the segments $AB$ and $AC$, respectively, so that $MN$ is parallel to $BC$ and tangent to the incircle of the triangle $ABC$. Let $K$ be the point where the incircle of the triangle $AMN$ is tangent to $MN$. It is known that $MN=4$, $BC=12$, and the segments $MK$ and $KN$ have integer lengths. Show that the triangle $ABC$ is equilateral or right.
Illustrative configuration only.
Illustrative configuration only.