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Question

O is the centre of the circle. AB is a minor arc of the circle. The angle subtended by AB at centre AOB = 110, then angle subtended by the arc at any point on the remaining part of the circle i.e. APB is (where P is any point on the circle)?


A

50

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B
45
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C
55
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D
65
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Solution

The correct option is C 55

As P is any point on the circle we can take that as shown in the figure.

Now we can easily see that in ΔPOB, OP=OB since both are radii of the circle.

So, OPB = OBP

As exterior angle is equal to sum of interior opposite angles,

we can write COB = OPB + OBP

= 2 OPB

So, COB = 2 CPB

Similarly, in ΔPOA, OP=OA since both are radii of the circle.

So, OPA = OAP

As the exterior angle is equal to the sum of interior opposite angles,

we can write COA = OPA + OAP

= 2 OPA


So COA = 2 CPA

Hence, COA+COB = 2(CPA + CPB)
Or, AOB = 2APB

Substituting we can get APB = 55.


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