Math Is Fun Forum

ncyaclauds

Member

Registered: 2016-06-18

Posts: 8

Geometry Help

Let
A_1, A_2 \cdots A_{12} be twelve equally spaced points on a circle with radius 1.

Find
(A_1 A_2)^2 + (A_1 A_3)^2 + \cdots + (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.)

I have tried this attempting this problem multiple times, however, I keep on getting the same answer. I keep on getting 24. Can you help me?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry Help

Hi;

This problem has been posted a couple of times on this forum and some advice given:

For an answer I am getting

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.