Question

an equilateral triangle ABC is inscribed in a circle of radius r units the ratio of area of the triangle ABC to the remaining part of the circle(exept the area occupied by the triangle) is.......

Answer 1

ABC is an equilateral triangle
∠ACD = 60°
∠OCD = ∠ACD / 2
            = 30°

In triangle OCD,
     cos 30°= CD / OC
=> √3 / 2   = 3 / r
=>  r = 3 x 2 /√3
         = 6 / √3
         = 2√3 cm
         = 3.4641 cm