Multiple choice

The length of a chord of a circle is equal to the radius of the circle. The angle this chord subtends in the major segment of the circle is equal to

  1. 30°

  2. 45°

  3. 55°

  4. 60°

  5. 70°
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A Correct answer
Explanation

A chord equal to the radius forms an equilateral triangle with the center. The central angle is 60 degrees. The angle subtended in the major segment is half the central angle, which is 30 degrees.

AI explanation

The chord and the two radii connecting its endpoints to the center form an equilateral triangle because all three sides are equal to the radius. This means the angle subtended by the chord at the center of the circle is 60 degrees. The angle subtended by a chord in the major segment is half the angle it subtends at the center, so the required angle is 60 / 2 = 30 degrees.

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