# Excirlce

Author: mathforces
Problem has been solved: 2 times

Русский язык | English Language

On the side $AC$ of the triangle $ABC$ with the incircle radius equal to $3$, the points $M$ and $N$ are chosen so that point $M$ is closer to point $A$ than point $N$ is. It turned out that the radii of the incircles of triangles $ABM$, $MBN$ and $NBC$ are all equal to $2$, and the radii of the excircles of these three triangles located opposite their common vertex $B$ are equal to $10$, $12$ and $6$, respectively. What is the radius of the excircle of the triangle $ABC$ located opposite the vertex $B$?