+0  
 
0
2
2
avatar+955 

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

 Dec 22, 2023
 #1
avatar+126665 
+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

 

 

 

cool cool cool

 Dec 22, 2023
 #2
avatar+26 
+1

The way you solved it was really easy to understand! Wow!

 Dec 22, 2023

3 Online Users

avatar