+0

# /gone

-2
151
4

/gone

Dec 16, 2019
edited by whoisjoe  Jan 7, 2020

#1
+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
0

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

Guest Dec 16, 2019
#2
-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
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