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Grade: 12th pass

                        

A regular hexagon $ a regular dodecagon are inscribed in the same circle.if the side of the dodecagon is (under root 2-1),then the side of the hexagon is?

2 years ago

Answers : (1)

Arun
24742 Points
							

For dodecagon sin(2π/40) = (a/2)/r     so    r = (a/2)/ sin(π/20)

now for hexagon sin(2π/12) = (x/2)/r       so x/2 = r sin(π/6)  =  (a/2) sin(π/6)/ sin(π/20)  

so  x  = (√3-1) (1/2) / ((√5-1)/4)                      here sin(π/20) = (√5-1)/4

or x = 4(√3-1) / 2(√5-1) 

now solve it for further simplification

2 years ago
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