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150 Questions 150 Marks 150 Mins
Given:
Chord of circle = Radius of circle
Concept:
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
If 2 angles are made on the same chord, then the angle at the center is twice the angle at circumference.
Calculation:
Chord of circle = Radius of circle
So, ΔAOB is an equilateral triangle (OA= OB = AB)
∠AOB = 60°
If 2 angles are made on the same chord, then the angle at the center is twice the angle at circumference.
⇒ ∠AOB = 2∠ACB
⇒ 60° = 2∠ACB
⇒ 30° = ∠ACB
The sum of either pair of opposite angles of a cyclic quadrilateral is 180°.
⇒ ∠ACB + ∠ADB = 180°
⇒ 30° + ∠ADB = 180°
⇒ ∠ADB = 150°
∴ The angle subtended by the chord which is equal to the radius at any point of the minor arc of the circle is 150°.
The correct option is 3 i.e. 150°
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