MathDB

There are distinct points

A_1, A_2, \dots, A_{2n}

with no three collinear. Prove that one can relabel the points with the labels

B_1, \dots, B_{2n}

so that for each

1 \le i < j \le n

the segments

B_{2i-1} B_{2i}

and

B_{2j-1} B_{2j}

do not intersect and the following inequality holds.

B_1 B_2 + B_3 B_4 + \dots + B_{2n-1} B_{2n} \ge \frac{2}{\pi} (A_1 A_2 + A_3 A_4 + \dots + A_{2n-1} A_{2n})

Problem Statement