Multiple choice

A chord of a circle is equal to its radius. The angle subtended by this chord at a point in major segment is

  1. $ { 60 }^{ o } $
  2. $ { 30 }^{ o } $
  3. $ { 120 }^{ o } $
  4. $ { 90 }^{ o } $
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B Correct answer
Explanation

A chord equal to the radius forms an equilateral triangle with the center, subtending 60 degrees at the center. By the circle theorem, the angle subtended at the circumference in the major segment is half the angle at the center, which is 60 / 2 = 30 degrees.

AI explanation

If the chord equals the radius, the triangle formed by the two radii and the chord is equilateral, meaning the central angle is 60 degrees. The angle subtended by this chord at a point in the major segment is an inscribed angle, which is half of the central angle subtending the same minor arc. Therefore, the angle is 60 divided by 2, which equals 30 degrees.

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