Question 72
Let $A_1, A_2, \dots, A_k$ be points on the unit circle. Prove that
$$
\sum_{1 \le i \lt j \le k} d(A_i, A_j)^2 \le k^2,
$$
where $d(A_i, A_j)$ denotes the distance between $A_i, A_j$.
$$
\sum_{1 \le i \lt j \le k} d(A_i, A_j)^2 \le k^2,
$$
where $d(A_i, A_j)$ denotes the distance between $A_i, A_j$.