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Q.

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?


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a

45°

b

90°

c

120°

d

180° 

answer is A.

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Detailed Solution

∠BOC=30° and ∠AOB=60° (Given)
⇒∠AOC= ∠AOB + ∠BOC
⇒∠AOC= 60°+30°
⇒∠AOC= 90°
We can see that AOC is the angle subtended by the arc ABC at its centre.
D is now the point on the circle that is not the arc ABC.
As a result, we know that the angle subtended by an arc at the centre is twice that of any other point on the circle.
Therefore,
⇒ ∠AOC = 2×∠ADC
⇒ 90° = 2×∠ADC
⇒90°2=∠ADC
⇒ 45°= ∠ADC
Hence we get the value of ∠ADC as 45°.
 
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