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Question

In the given figure, A, B and C are three points on a circle with centre O such that BOC=30 and AOB=60. If D is a point on the circle other than the arc ABC, find ADC.

A
(902)
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B
45
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C
(602)
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D
30
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Solution

The correct options are
A (902)
B 45
It can be observed that
AOC=AOB+BOC=60+30=90

We know that angle subtended by an arc at the center is double the angle subtended by it any point on the remaining part of the circle.

So,ADC=12AOC
=12×90=45

ADC=45.

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Angles subtended by an arc at the centre is twice the angle subtended at the circumference
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