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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

 Sep 14, 2024
 #1
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Let's note that P1P2+P2P3+P3P4++P9P10+P10P1 is simply the perimeter of the decagon

We also know that radius/2(1+5) is one of the sidelenghts. Thus, we can find the perimeter easily. 

 

The perimeter is just

10(1/2)(1+5)=5(1+5)6.18

 

Thanks! :)

 Sep 17, 2024
edited by NotThatSmart  Sep 17, 2024

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