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
\(P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1 \)
This is just the perimemter of a decagon
The length of one side can be found as radius/2 ( -1 + sqrt (5))
The perimeter is 10 (1/2) ( -1 + sqrt 5) = 5 ( -1 + sqrt 5) ≈ 6.18
The way you solved it was really easy to understand! Wow!
+1459 
