The arc ABC of a circle with centre O subtends 132 at the centre The chord AB is extended to t...........

Quantitative Aptitude (CGL) Geometry

The arc ABC of a circle with centre O subtends 132 at the centre. The chord AB is extended to the point P. The angle $\angle$ CBP is equal to

This questions was previously asked in

SSC CGL 12 June 2019 Shift-2

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48^o

66^o

76^o

68^o

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Explanation:

As per the given question,
Angle subtended by the arc =132^o
Now,

As we know, from the property of circle,
2 × ∠ADC = ∠AOC
⇒ 2 × ∠ADC = 132^o
132^o
⇒ ∠ADC = 2
⇒ ∠ADC = 66^o − − − − − − − − − − − − − − − −(i)

Now, ABCD is a cyclic quadrilateral,
So as the property of the cyclic quadrilateral
∠ADC + ∠ABC = 180^o
⇒ ∠ABC = 180^o − ∠ADC
⇒ ∠ABC = 180^o − 66^o = 114 ^o − − − − − − − − − − − − − − − − − − − (ii)
We know that angle subtended on the straight line = 180°
Now, ∠ABC + ∠CBP = 180^o
∠CBP = 180^o− ∠ABC = 180^o − 114^o = 66^o
⇒ ∠CBP = 66^o