Both inscribable in and circumscribable about a circle
Source: IMO Shortlist 1989, Problem 14, ILL 48
September 18, 2008
geometrycircumcirclequadrilateralcollinearityIMO Shortlist
Problem Statement
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.