+0

0
144
5
+941

Aug 12, 2020

#1
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
+941
0

Sorry but thats inncorrect

qwertyzz  Aug 12, 2020
#3
+1154
+4

I think It's 12^2=144 am I right?

Aug 12, 2020
#4
+941
0

Yes!  Thank you!!

qwertyzz  Aug 12, 2020
#5
+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 \(1 \le i < j \le 12\).