IMO 1979 LL NET48

Origin: NET

Problem

In the plane a circle C of unit radius is given. For any line l a number s(l) is defined in the following way: If l and C intersect in two points, s(l) is their distance; otherwise, s(l) = 0. Let P be a point at distance r from the center of C. One defines M(r) to be the maximum value of the sum s(m) + s(n), where m and n are variable mutually orthogonal lines through P. Determine the values of r for which M(r) > 2.