# In a circle with center O and radius 1 cm | Quantitative Aptitude - Geometry – Circles

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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Circles : In a circle with center O and radius 1 cm . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

## CAT 2018 - Slot-1 - Circles - Question-4 - In a circle with center O and radius 1 cm

Q. 4: 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?

1. (π/6)^(1/2)

2. (π/(4√3))^(1/2)

3. (π/(3√3))^(1/2)

4. (π/4)^(1/2)

As OC =OD so angle OCD = angle ODC =(180 -60)/2 = 60

So triangle OCD is an equilateral triangle,

Area of OCD = √3/4 OC^2 = 1/6×π×1^2

OC^2 = π/(3√3)

So OC= (π/(3√3))^(1/2)

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