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# A regular dodecagon is inscribed in a circle with radius 1. Compute (The sum includes all terms of the form where )

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A regular dodecagon \(P_1 P_2 P_3 \dotsb P_{12}\) is inscribed in a circle with radius 1. Compute \((P_1 P_2)^2 + (P_1 P_3)^2 + \dots + (P_{11} P_{12})^2.\)
(The sum includes all terms of the form \((P_i P_j)^2,\) where \(1 \le i < j \le 12.\))

432, 42, 55, 44, 24-12*sqrt3, 12sqrt3

Apr 11, 2020