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Question 2 :In a circle with centre 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

- \\frac{π}{4})
^{\\frac{1}{2})} - \\frac{π}{6})
^{\\frac{1}{2})} - \\frac{π}{4√3})
^{\\frac{1}{2})} - \\frac{π}{3√3})
^{\\frac{1}{2})}

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Given ∠AOB = 60°

Area of Sector AOB = \\frac{60}{360}) × π × 12 = \\frac{π}{6}) ---(1)

Given OC = OD => ∠OCD = ∠ODC = 60°

△OCD is an Equilateral Triangle with side = a

Area(△OCD) = \\frac{√3}{4}) × a × a ---(2)

Its given that Area(OCD) = \\frac{1}{2}) × Area(OAB)

a^{2}\\frac{√3}{4}) = \\frac{π}{6×2})

a = **(\\frac{π}{3√3})) ^{\\frac{1}{2})}**

The question is **"In a circle with centre 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" **

Choice D is the correct answer.

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