# Cyclic Q

Author: mathforces
Problem has been solved: 16 times

Русский язык | English Language

In the cyclic quadralateral $MHFS$, the lengths of the sides $MH = 10$, $HF = 8$, $SF = 25$, $MS = 12$ are known. Let $x$ be the radius of the circle which is tangent to the segments $MS$, $MH$ and $FH$. It is known that $x$ can be represented as a fraction of $\frac{b\sqrt{a}}{\sqrt{c}}$, for some pairwise coprime positive integer numbers $a$, $b$ and $c$. What is $a + b + c$ equal to?