If ABCD IS A PARALLELEOGRAM G IS THE INTERSECTION POINT of diagonal of parallel eogram abd O is any point OA+ OB + OC+ OD In vector

Question

In a circle with centre O and radius 1cm, an arc AB makes an angle of 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

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If ABCD IS A PARALLELEOGRAM G IS THE INTERSECTION POINT of diagonal of parallel eogram abd O is any point OA+ OB + OC+ OD In vector

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Question : O is a point in the interior of $△ ABC$ such that OA = 12 cm, OC = 9 cm, $∠ A O B = ∠ B O C = ∠ C O A$ and $∠ A B C = 60^{\circ}$ . What is the length (in cm) of OB?
Option 1: $6 \sqrt{3}$
Option 2: $4 \sqrt{6}$
Option 3: $4 \sqrt{3}$
Option 4: $6 \sqrt{2}$