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

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) (Ï€/6)^(1/2)
b) (π/(4√3))^(1/2)
c) (π/(3√3))^(1/2)
d) (Ï€/4)^(1/2)

Answer: c)  (π/(3√3))^(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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