CAT 2018 Geometry & Mensuration Question (Hard)

Question

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

Accepted Answer

Step 1 Area of Sector AOB Angle at center 60 Radius 1 cm Area of sector AOB _ 360 circ cdot pi r 2 360 cdot pi cdot 1 2 6 --- Step 2 Area of triangle OCD COB 60 since OC and OD lie along OA and OB. Triangle OCD is isosceles with angle between sides OC and OD 60 . So, _ triangle OCD 2 cdot OC cdot OD

CAT 2018

Quantitative

Geometry & Mensuration

Hard

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