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. geometry unsolvedgeometry