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Cyclic Areas

Author: mathforces
Problem has been solved: 20 times

Русский язык | English Language



Point $ X $ lies inside triangle $ ABC $. Lines $ AX $, $ BX $ and $ CX $ intersect the sides of the triangle at points $ A_1 $, $ B_1 $ and $ C_1 $, respectively. Denote by $ (MNK) $ the area of the triangle $ MNK $. It is known that $ (XBA_1) = 27 $, $ (XCA_1) = 18 $, $ (XCB_1) = 20 $, $ (XAB_1) = 40 $. What is the area of triangle $ ABC $?





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