... CD at X, and a circle through C, D touches19 Geometry Problems Amir Hossein Parvardi ∗January 9, 2011Edited by: Sayan Mukherjee.Note. Most of problems have solutions. Just click on the number ... ABCD whose faces are all congruent. Thevertices A, B, C lie in the positive part of x-axis, y-axis, and z-axis, respectively,and AB = 2l − 1, BC = 2l, CA = 2l + 1, where l > 2. Let the volume ... S be the set of all polygonal surfaces in the plane (a polygo-nal surface is the interior together with the boundary of a non-self-intersectingpolygon; the polygons do not have to be convex)....