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
Suppose O is the centre of the circle. Then ΔOP1P2 is an isosceles triangle with OP1=OP2=1 and .
Then . Note that . Then .
Repeating the same process 10 times gives .