MathDB

Let

ABCD

be a tetragonal.
(a) If the plane

(P)

cuts

ABCD,

find the necessary and sufficient condition such that the area formed from the intersection of the plane

(P)

and the tetragonal be a parallelogram. Prove that the problem has three solutions in this case.
(b) Consider one of the solutions of (a). Find the situation of the plane

(P)

for which the parallelogram has maximum area.
(c) Find a plane

(P)

for which the parallelogram be a lozenge and then find the length side of his lozenge in terms of the length of the edges of

ABCD.

Problem Statement