## Τετάρτη, 2 Αυγούστου 2017

### 1991 IMO Problem 1 (USS)

Given a triangle ABC, let I be the center of its inscribed circle. The internal bisectors of the angles A,B,C  meet the opposite sides in A’, B’ , C’ respectively. Prove that  $$\frac{1}{4}<\frac{AI\cdot BI\cdot CI}{AA'\cdot BB'\cdot CC'}\le \frac{8}{27}$$
$$\frac{1}{4}<\frac{AI\cdot BI\cdot CI}{AA'\cdot BB'\cdot CC'}\le \frac{8}{27}$$