SOLUTION: 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

SOLUTION: 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

Question 1210570: 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
Answer by ikleyn(53617) (Show Source): You can put this solution on YOUR website!
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Let P_1 P_2 P_3 ... 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 + . . . + P_9 P_{10} + P_{10} P_1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If this sum

P_1 P_2 + P_2 P_3 + P_3 P_4 + . . . + P_9 P_{10} + P_{10} P_1

is the sum of vectors, then this sum is equal to zero - as any sum of vectors along a closed contour.

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