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CAT 2018 Slot 1 — QA Question 17

Basics of CirclesEasy

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

Answer & solution

  • A

    (π/6)1/2

  • (π/3√3)1/2

  • C

    (π/4√3)1/2

  • D

    (π/4)1/2

Solution

Let OC = OD = x

△OCD is an equilateral triangle of side x. [All angles are 60 degree.]

A(△OCD) = 34x2

A(sector O-AB) = 60360×π(1)2 = π6

By the given condition,

34x2 = 12×π6

∴ x2 = π33

∴ x = (π33)1/2

Hence, option (b).

CAT 2018 Slot 1 QA Q17: 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 bound — Solution | TheCATExam