Multiple choice

A chord $AB$ of a circle of radius $20\ cm$ makes a right angle at the centre of the circle. What is the area of the minor segment in $cm^{2}$?

  1. $31.4$
  2. $57$
  3. $62.8$
  4. $114$
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D Correct answer
Explanation

Area of sector = (90/360) * pi * r^2 = 1/4 * 3.14 * 400 = 314. Area of triangle = 1/2 * r * r = 1/2 * 20 * 20 = 200. Area of minor segment = 314 - 200 = 114.

AI explanation

The area of the minor segment is found by subtracting the area of the triangle from the area of the 90-degree sector. The sector area is (90/360) * (22/7) * 20^2 = 314.28 sq cm, and the right-angled triangle area is (1/2) * 20 * 20 = 200 sq cm. The difference between these two areas is 114.28 sq cm, which rounds to 114.

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