a) Easy. We have to finish just one non-trivial case when we put AB, CD and for example AC in one colour. Easy to see that AB+BC+CD+DA>2d (d is the diagonal), so AD+BC>d (they make the triangle) or AB+CD>d. In the second case we should prove that CD+d>AB (and we have AD+BC<d). Since d>AD+BC, we have that CD+d>CD+AD+BC>AB. b) No. For example, take AB=5, CD=0.4 and AD=2, for the right angle <BAD and put AB, CD and BD in the same colour.