Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1
This is just the perimeter of a decagon
One side, s, can be found by the Law of Cosines
s^2 = 1^2 + 1^2 2(1*1)cos 36°
s^2 = 2 -2 cos (36°)
s = sqrt [ 2 - 2 cos (36° ]
Perimeter =
10 sqrt [ 2 -2 cos (36°)] ≈ 6.18
+1167 
