... alternative proof ofStep 1.A1A2C′ A1A2CC′C′, A1, A2, QPage 13G5. For any set of five points in the plane, no three of which are collinear, let and denote the greatest and smallest ... points from. What is the minimum possible value of ?SM(S) m(S)SM(S) / m(S)Solution.When the five points are arranged at the vertices of a regular pentagon, it is easy to check that equals ... arbitrary configuration, and label the points and , so that hasmaximal area . In the following five steps, we prove the claim by showing that sometriangle has area or smaller.SA, B, C, DE ABCM...