Exams › SSC CGL (Prelims) › General

A chord in a circle of radius 12 cm subtends an angle of 120° at the center. What is the area of the minor segment?

1. (48\pi - 36\sqrt{3}) sq. cm
2. (36\pi - 48\sqrt{3}) sq. cm
3. (60\pi - 36\sqrt{3}) sq. cm
4. (72\pi - 36\sqrt{3}) sq. cm

Correct answer: (48\pi - 36\sqrt{3}) sq. cm

Solution

The minor segment equals the area of the sector minus the area of the triangle formed by the two radii and the chord. For radius 12 cm and angle 120°, sector area = \(\frac{120}{360}\pi(12)^2 = 48\pi\), and triangle area = \(\frac12(12)^2\sin120^\circ = 36\sqrt{3}\). So the segment area is \(48\pi - 36\sqrt{3}\) sq. cm.

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