Multiple choice

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to

  1. 300

  2. 450

  3. 600

  4. 900
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A Correct answer
Explanation

If chord length equals radius, the triangle formed by the chord and the center is equilateral. The angle at the center is 60 degrees. The angle subtended by the chord on the major arc is half the angle at the center, which is 30 degrees.

AI explanation

The chord and the two radii at its ends form an equilateral triangle, so the central angle is 60 degrees. The angle subtended by this chord on the longer segment (the major arc) is an angle in the alternate segment, which equals half the central angle of the minor arc. Thus, the angle is 60 / 2 = 30 degrees.

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