Exams › SSC CGL (Prelims) › General

What is the area of the segment formed by a chord in a circle of radius 10 cm, if the angle subtended at the center is \(90^\circ\)?

1. 25 π - 25√2
2. 50 π - 50
3. 50 π - 25√2
4. 25 π - 50

Correct answer: 25 π - 50

Solution

The segment area equals the area of the 90° sector minus the area of the triangle formed by the two radii and the chord. With radius 10 cm, the sector area is \(25\pi\) and the triangle area is 50, so the segment area is \(25\pi-50\).

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