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

CAT 2018 – The CAT QA section has grown increasingly difficult since 2015. In order to tackle the tougher CAT Level QA questions for the CAT Exam, it is important to understand the basics of CAT. To obtain a great CAT score, make use of MBAP Free Study material with detailed solutions and video explanations. Check out MBAP free Mock test to take these questions in a test format for free.

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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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