Let O be a point of three-dimensional space and let l1,l2,l3 be mutually perpendicular straight lines passing through O. Let S denote the sphere with center O and radius R, and for every point M of S, let SM denote the sphere with center M and radius R. We denote by P1,P2,P3 the intersection of SM with the straight lines l1,l2,l3, respectively, where we put Pi=O if li meets SM at two distinct points and Pi=O otherwise (i=1,2,3). What is the set of centers of gravity of the (possibly degenerate) triangles P1P2P3 as M runs through the points of S? geometry3D geometrysphereIMO LonglistIMO Shortlist