IMO 1966 LL ROM17

Origin: ROM

Problem

Suppose ABCD and A′B′C′D′ are two parallelograms arbi- trarily arranged in space, and let points M, N, P, Q divide the segments AA′, BB′, CC′, DD′ respectively in equal ratios. (a) Show that MNPQ is a parallelogram; (b) Find the locus of MNPQ as M varies along the segment AA′.