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The chord of a circle is equal to its radius. The angle (in degrees) subtended by this chord at any point on the minor arc of the circle is:
Question

The chord of a circle is equal to its radius. The angle (in degrees) subtended by this chord at any point on the minor arc of the circle is:

A.

130

B.

140

C.

150

D.

120

Correct option is C


Given:

A chord of a circle is equal in length to the radius of the circle.

Theorem Used:

​The angle subtended by a chord at any point on the minor arc is half the angle subtended by the same chord at the center of the circle.

Solution:

∠ACB = ½ ∠AOB = ½ × 60° = 30°

∠ACB + ∠ADB = 180° (Opposite angles of a cyclic quadrilateral)

∠ADB = 180° - 30° = 150°

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