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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?





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