🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


🎉Effortlessly calculate your score with the 2IIM Score Calculator!🎉

CAT 2018 Question Paper | Quants Slot 1

CAT Previous Year Paper | CAT Geometry Questions | Question 2

One of the important aspects of CAT Online Preparation is solving CAT Previous year Paper . This question entails CAT Geometry concepts. Arcs, radii, triangles – what not? A typical CAT Geometry question from CAT Previous Year Paper, which would help you gain confidence after solving. Give it a try and watch the video solution.

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})

🎉 Ace XAT 2025 with 2IIM's Crash Course - Enrol now


Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.

🎉Effortlessly calculate your score with the 2IIM Score Calculator!🎉


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

Method of solving this CAT Question from Geometry
Geometry - Finding the length of OC

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.

 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com