IMO Shortlist 1989 problem 14
Dodao/la: arhiva2. travnja 2012.
A bicentric quadrilateral is one that is both inscribable in and circumscribable about a circle, i.e. both the incircle and circumcircle exists. Show that for such a quadrilateral, the centers of the two associated circles are collinear with the point of intersection of the diagonals.
Izvor: Međunarodna matematička olimpijada, shortlist 1989