# Cyclic Areas

Author: mathforces
Problem has been solved: 26 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 $ABC$?