Just to complete the formailty: If r is the radius of the outer circle then radius of the inner circle = rsin(β/2). The required ratio = ∏(rsin(β/2)^2 /[∏(r)^2 ∏(rsin(β/2)^2] = [tan(β/2)]^2 and [(1-cos(β)]/[(1+cos(β)] can also be shown = [tan(β/2)]^2 by the half angle formula. Hence etc. Ajit
(1+cos)/(1-cos)? YU
ReplyDeleteNow it is (1-cos)/(1+cos).
ReplyDeleteSorry that was a typo.
ReplyDeleteJust to complete the formailty: If r is the radius of the outer circle then radius of the inner circle = rsin(β/2). The required ratio = ∏(rsin(β/2)^2 /[∏(r)^2 ∏(rsin(β/2)^2] = [tan(β/2)]^2 and [(1-cos(β)]/[(1+cos(β)] can also be shown = [tan(β/2)]^2 by the half angle formula. Hence etc.
ReplyDeleteAjit