# Small triangle

Author: mathforces
Problem has been solved: 13 times

Русский язык | English Language

The area of the triangle $ABC$ is 1. The cevian $CG$ intersects the cevians $AE$ and $BF$ at the points $T$ and $S$ respectively, and the segments $BF$ and $AE$ intersect at the point $R$. It turned out that the points $T$, $R$ and $S$ are the midpoints of the segments $AE$, $BF$ and $CG$, respectively. The area of the triangle $STR$ can be represented as a fraction $\frac{a-b \sqrt{c}}{d}$, where $a, b, c, d$ are pairwise coprime positive integer numbers. Find $abcd$.