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Consider eight points that are equally spaced on a circle in which the length of the radius is 1.  Find the product of the distances from one of the points to each of the other seven points.

 Dec 17, 2019
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We can let the eight points be

 

A = (1,0)   B  = (1/√2 , 1/√2) C  =  (0, 1)  D  = (-1/√2, 1/√2)  E  = (0, -1)

F  = (-1/√2, -1/√2)   G  =  (0, -1)    H  = (1/√2, -1/√2)

 

Let A  be the selected  point  that we will use to calculate the distances to every other point

 

We can use the distance formula to calculate the distance from A to the other seven points [which you should be able to work with  ]

 

I will  use  WolframAlpha  to calculate these

AB  =  √ [ 2 -√2]

AC = √2

AD  = √[2 + √2 ]

AE  =  2

AF  = √[2 + √2 ]

AG = √2

AH  = √[2 - √2]

 

 

And computing these  products we have

 

2 * √2 * √2  * (√[2 - √2])^2  * ( √[2 + √2] )^2  =

 

2 * 2   *  ( 2 - √2) ( 2 + √2)  =

 

4  *  [ 4  - 2  ]  =

 

4 *  2   =

 

8

 

 

cool cool cool

 Dec 17, 2019

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