MathDB

Let

A,B,C,M

points in the plane and no three of them are on a line. And let

A',B',C'

points such that

MAC'B, MBA'C

and

MCB'A

are parallelograms: (a) Show that \overline{MA} \plus{} \overline{MB} \plus{} \overline{MC} < \overline{AA'} \plus{} \overline{BB'} \plus{} \overline{CC'}. (b) Assume segments

AA', BB'

and

CC'

have the same length. Show that 2 \left(\overline{MA} \plus{} \overline{MB} \plus{} \overline{MC} \right) \leq \overline{AA'} \plus{} \overline{BB'} \plus{} \overline{CC'}. When do we have equality?

Problem Statement