## Slot -2 – Quantitative Aptitude – Geometry – Circles – A chord of length 5 cm subtends an

A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is?

a) 6√2

b) 8

c) 4√2

d) 5√3

Solution: In triangle ODA, OA=AD cosec 30=5

So if the angle AOB is 120 degree, then angle AOD will be 120/2=60

In the case length of chord = 2×OA Sin 60=5√3

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

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?

a) (π/6)^(1/2)

b) (π/(4√3))^(1/2)

c) (π/(3√3))^(1/2)

d) (π/4)^(1/2)

Solution: 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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## Slot -1 – Quantitative Aptitude – Geometry – Circles – In a circle, two parallel chords on the same side

In a circle, two parallel chords on the same side of diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is?

a) √11

b) √13

c) √12

d) √14

Solution: Option b) √13 is correct

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
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