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:
Option 1: 130°
Option 2: 140°
Option 3: 150°
Option 4: 120°
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Correct Answer: 150°
Solution :
Let the AB chord of the circle = The radius of the circle
⇒ $\triangle AOB$ is an equilateral triangle (OA = OB = AB)
⇒ $∠AOB = 60°$
If 2 angles are made on the same chord, then the angle at the centre is twice the angle at the circumference.
⇒ $∠AOB = 2∠ACB$
⇒ $60° = 2∠ACB$
⇒ $ ∠ACB=30°$
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
⇒ $∠ACB + ∠AEB = 180°$
⇒ $30° + ∠AEB = 180°$
⇒ $∠AEB = 150°$
Hence, the correct answer is 150°.
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