What is the angle substandard by the arc at the Centre if the length of the arc of a circle is equal to the radius of the circle?

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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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