IMO Shortlist 1982 problem 8
A convex, closed figure lies inside a given circle. The figure is seen from every point of the circumference at a right angle (that is, the two rays drawn from the point and supporting the convex figure are perpendicular). Prove that the center of the circle is a center of symmetry of the figure.
Source: Međunarodna matematička olimpijada, shortlist 1982