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Let $a_1$, $a_2$, $\dots$, $a_{12}$ be twelve equally spaced points on a circle with radius 1. find\[(a_1 a_2)^2 + (a_1 a_3)^2 + \dots + (a_{11} a_{12})^2.\](the sum includes the square of the distance between any pair of points, so the sum includes $\binom{12}{2} = 66$ terms.)

1 Answer

3 votes

The sum evaluates to 144. See the linked question in the comments for details.

User Sandip Solanki
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