Question

a regular hexagon and a regular dodecagon are inscribed in a same circle if the side of a dodecagon is ✓3-1 then the side of hexagon is

Answer 1

I hope it would help you to get the answer!!!

We have, for dodecagon sin(2π/40) = (a/2)/r     

so, r = (a/2)/ sin(π/20)

and for hexagon sin(2π/12) = (x/2)/r       

so, x/2 = r sin(π/6)  =  (a/2) sin(π/6)/ sin(π/20)  

Now solve for x, you'll get the answer.