+0  
 
-2
151
4
avatar+30 

/gone

 Dec 16, 2019
edited by whoisjoe  Jan 7, 2020
 #1
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+1

There are 12 digaonals that have a length of P_1 P_2, which from the Sine Law, is sin (15 degrees).  There are 12 diagonals that have a legnth of P_1 P_3, which from the Sine Law, is sin (30 degrees).  We can appy the same reasoning to the other diagonals, which gives us a total sum of

 

(12 sin 15)^2 + (12 sin 30)^2 + (12 sin 45)^2 + (12 sin 60)^2 + (12 sin 75)^2 + (12 sin 90)^2 + (12 sin 105)^2 + (12 sin 120)^2 + (12 sin 135)^2 + (12 sin 150)^2 + (12 sin 175)^2 = 864.

 Dec 16, 2019
 #3
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0

Oh, I double-counted!  I need to divide that by 2, so the answer is 864/2 = 432.

Guest Dec 16, 2019
 #2
avatar+30 
-1

Hm. The way I was thinking about it didn't involve sin/cos however. Also, I believe this answer is incorrect. One of the hints given is:

" Sums of squares of lengths should make you think of what?"

 Dec 16, 2019
 #4
avatar+108790 
0

If you have hints you should share them with the answerers right froom the very beginning.

 

Why should answerers have less information than you do ?

Melody  Dec 16, 2019

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