# 4 days to 2016 Tetrahdron problem

Geometry Level 5

In tetrahedron $$SABC$$, the circumcircles of faces $$SAB$$, $$SBC$$, and $$SCA$$ each have radius 108.

The inscribed sphere of $$SABC$$, centered at I, has radius 35. Additionally, $$SI = 125$$. Let $$R$$ is the largest possible value of the circumradius of face $$ABC$$.

Given that $$R$$ can be expressed in the form $$\sqrt{ \dfrac{m}{n} }$$, where $$m$$ and $$n$$ are relatively prime positive integers. Find $$m + n$$.

×