IMO Shortlist 1981 problem 17
Dodao/la:
arhiva2. travnja 2012. Three circles of equal radius have a common point
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
and lie inside a given triangle. Each circle touches a pair of sides of the triangle. Prove that the incenter and the circumcenter of the triangle are collinear with the point
![O](/media/m/9/6/0/9601b72f603fa5d15addab9937462949.png)
.
%V0
Three circles of equal radius have a common point $O$ and lie inside a given triangle. Each circle touches a pair of sides of the triangle. Prove that the incenter and the circumcenter of the triangle are collinear with the point $O$.
Izvor: Međunarodna matematička olimpijada, shortlist 1981