MathForces: Math Olympiads
MathForces - Math Olympiadsβeta
Login Register

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 $.





Sorry, you need to login into your account