CAT 2018 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Geometry Questions | Question 2

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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

1. $$frac{π}{4}$$\frac{1}{2}$ 2. $\frac{π}{6}$$\frac{1}{2}$ 3. $\frac{π}{4√3}$$\frac{1}{2}$ 4. $\frac{π}{3√3}$$\frac{1}{2}$ 2IIM : Best Online CAT Coaching 2IIM's Crash Course CAT 2019 Introductory price @ 7500 Till Oct 7CAT Online Coaching Video Explanation Best CAT Coaching in Chennai CAT Coaching in Chennai - CAT 2020Starts Sat, October 5th, 2019 Explanatory Answer Method of solving this CAT Question from Geometry Given ∠AOB = 60° Area of Sector AOB = $\frac{60}{360}$ × π × 12 = $\frac{π}{6}$ ---$1)
Given OC = OD => ∠OCD = ∠ODC = 60°
△OCD is an Equilateral Triangle with side = a
Area(△OCD) = $$frac{√3}{4}$ × a × a ---$2)
Its given that Area(OCD) = $$frac{1}{2}$ × Area$OAB)
a2$$frac{√3}{4}$ = $\frac{π}{6×2}$ a =$$$frac{π}{3√3}$)$\frac{1}{2}$ The question is "In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is" Hence, the answer is $\frac{π}{3√3}$$\frac{1}{2}$ cm Choice D is the correct answer. 2IIM's CAT CoursesDussehra Discount of 25% Till Oct 9CAT Online Coaching Signup Now! Already have an Account? CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Oct 5th, 2019 Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 How to reach 2IIM? Phone:$91) 44 4505 8484
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