Consider a cube ABCDA′B′C′D (with AB⊥AA′∥BB′∥CC′∥DD). Let X be an inner point of the segment AB and denote Y the intersection of the edge AD and the plane B′D′X.
(a) Let M=B′Y∩D′X. Find the locus of all Ms.
(b) Determine whether there is a quadrilateral B′D′YX such that its diagonals divide each other in the ratio 1:2. geometry3D geometryratioLocuscube