Found problems: 1
2008 Grigore Moisil Intercounty, 3
Let $ A_1,B_1,C_1 $ be points on the sides (excluding their endpoints) $ BC,CA,AB, $ respectively, of a triangle $ ABC, $ such that $ \angle A_1AB =\angle B_1BC=\angle C_1CA. $ Let $ A^* $ be the intersection of $ BB_1 $ with $ CC_1,B^* $ be the intersection of $ CC_1 $ with $ AA_1, $ and $ C^* $ be the intersection of $ AA_1 $ with $ BB_1. $ Denote with $ r_A,r_B,r_C $ the inradii of $ A^*BC,AB^*C,ABC^*, $ respectively. Prove that
$$ \frac{r_A}{BC}=\frac{r_B}{CA}=\frac{r_C}{AB} $$
if and only if $ ABC $ is equilateral.
[i]Daniel Văcărețu[/i]