MathForces: Math Olympiads
MathForces - Math Olympiadsβeta
Login Register

Cyclic Q

Author: mathforces
Problem has been solved: 9 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?





Sorry, you need to login into your account