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Question

In the given figure, if the angle between two radii of a circle is 120, then find PAO.


A
90
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B
45
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C
30
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D
60
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Solution

The correct option is C 30


Given POQ = 120

Consider quadrilateral POQA,

POQ + OQA + QAP + APO = 360 -------(1)

[By Theorem - The tangent at any point of a circle is perpendicular to the radius through the point of contact]

So, OQA = APO = 90

On substituting these values in (1) we get,

120 + 90 + QAP + 90 = 360

QAP = 360 - 120 - 90 + 90

QAP = 60

Draw a line joining point A and O.

[By Theorem - The centre of a circle lies on the bisector of the angle between two tangents drawn

from a point outside it]

so, line AO bisects QAP

PAO = QAO

So, QAP = PAO + QAO

QAP = 2 × PAO

60 = 2 × PAO

PAO = 602

PAO = 30


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