# Inverse Sum in Triangle

Author: mathforces
Problem has been solved: 10 times

Русский язык | English Language

Let $O$ be the center of the circumscribed circle of the triangle $ABC$ with sides 9, 10, and 11. The lines $AO$, $BO$ and $CO$ intersect the sides $BC$, $AC$ and $AB$ at the points $M$ , $N$ and $K$ respectively. It is known that the sum $\frac{1}{AM}+\frac{1}{BN}+\frac{1}{CK}$ can be represented in the (simpliest) form $\frac{a \sqrt{b}}{c}$, for some positive integer numbers $a$, $b$ and $c$. What is $ac + b$ equal to?