Question
A regular hexagon and a regular dodecagon are inscribed in the same circle. if the side of the dodecagon is (√3-1), then the side of hexagon is
Joshi sir comment
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