Problem #287
Heptagonal Distances
Let there be a regular Heptagon inscribed in a circle of radius 357 units. Find the sum of the square of distances between all pairs of vertices of the Heptagon.In other words, let v_1,v_2,v_3 ... v_7 be the vertices of the Heptagon, and D_{ij} be the distance between vertex v_i and v_j. Find S=\sum_{1\leq i < j \leq 7} D_{ij}^2