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Excirlce

Author: mathforces
Problem has been solved: 2 times

Русский язык | English Language



On the side $ AC $ of the triangle $ ABC $ with the incircle radius equal to $ 3 $, the points $ M $ and $ N $ are chosen so that point $ M $ is closer to point $ A $ than point $ N $ is. It turned out that the radii of the incircles of triangles $ ABM $, $ MBN $ and $ NBC $ are all equal to $ 2 $, and the radii of the excircles of these three triangles located opposite their common vertex $ B $ are equal to $ 10 $, $ 12 $ and $ 6 $, respectively. What is the radius of the excircle of the triangle $ ABC $ located opposite the vertex $ B $?





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