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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Question : The angle subtended by a chord on the major arc of the circle is 50°. What is the angle subtended by the same chord on the centre of the circle?
Question : The angle subtended by a chord on the centre of a circle is 180°. What will be the angle subtended by the same chord on the circumference of this circle?
Question : The length of the chord AB of a circle is equal to the radius of the circle. What will be the angle subtended by the chord at the centre of the circle?
Question : If the angle made by a chord on the major arc of a circle is $50^{\circ}$, then what will be the angle made by the same chord on the minor arc of this circle?
Question : The sum of the angles made by a chord at the centre and on the major arc of a circle is 225°. What will be the angle made at the major arc of this circle?
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