+2653 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
+1892 mmm...take a look at the points given.
\(P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1\)
This is essentially just the perimeter of the decagon \(P_1P_2P_3P_4P_5...P_{10}\)
The lenngth of one side is essentially
\(radius/2 ( -1 +\sqrt 5)\)
Now that we know one side, we can find the perimeter through the equation
\(10 (1/2) ( -1 + \sqrt 5) = 5 ( -1 + \sqrt 5) ≈ 6.18\)
Thus, the answer is 6.18,
Thanks! :)
