+0  
 
0
144
5
avatar+941 

Please help I can't figure this out

 Aug 12, 2020
 #1
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0

We can use the sine law to find P1 P2

 

By the sine law, P1 P2 = sin 15.  We can also find P1 P_3 = sin 60, P1 P4 = sin 90, etc.

 

So (P1 P2)^2 + (P1 P3)^2 + … + (P11 P12)^2 = 12 (sin 15)^2 + 12 (sin 30)^2 + 12 (sin 45)^2 + … + 12 (sin 90)^2 = 42.

 Aug 12, 2020
 #2
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Sorry but thats inncorrect 

qwertyzz  Aug 12, 2020
 #3
avatar+1154 
+4

I think It's 12^2=144 am I right?

 Aug 12, 2020
 #4
avatar+941 
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Yes!  Thank you!!

qwertyzz  Aug 12, 2020
 #5
avatar+25595 
+2

A regular dodecahedron \(P_1 P_2 P_3 \dotsb P_{12}\) is inscribed in a circle with radius 1.
Compute  \((P_1 P_2)^2 + (P_1 P_3)^2 + \dots + (P_{11} P_{12})^2\).
(The sum includes all terms of the form \((P_i P_j)^2\), where \(1 \le i < j \le 12\).

 

My answer see here: https://web2.0calc.com/questions/plshelp#r7

 

laugh

 Aug 13, 2020

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