DelSingh wrote:

O is the center of the circle above, OB=2, and angle AOB measures 120 degrees. What is the area of the triangular region AOB?

a) 1

b) 2

c) (sq root 3) /2

d) sq root 3

e) 2(sq root 3)

Source: GMAT Prep Question Pack 1

Difficulty: Hard

SINCE ANGLE AT CENTRE = \(120\)

when you draw perpendicular OC on AB

it divides in two equal \(30 - 60 - 90\) triangle see figure

sides are in ratio of\(1: \sqrt{3}: 2\)

therefore OC = \(1\) and \(CA = CB = \sqrt{3}\)

THEREFORE AB = \(2\sqrt{3}\)

Hence AREA Of triangle = \(1/2*base*height\)

= \(1/2 * 2\sqrt{3}*1 = \sqrt{3}\)

hence D

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