In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points
on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
Radius of the circle = 1 cm
Chord AB subtends an angle of 60° on the centre of the circle. R is the region bounded by the radii OA, OB and the arc AB.
R = 60°/360° × Area of the circle
= 1/6 × π × (1)2
= π/6 sq. cm
Given that OC = OD and area of triangle OCD is half that of R.
Area of triangle OCD = 1/2 × OC × OD × sin 60°
π/6 × 1/2 = 1/2 × OC × OC × √3/2
⇒ OC2 = π/3√3
The correct option is A.