    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 circle ∠APB is [P is any point on the circle]

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Solution

## The correct option is C  As P is any point on the circle, we can take that as shown in the figure. Now, we can easily see that in △POB, OP = OB since both are radii of the circle. So, ∠OPB =∠OBP As external angle is equal to sum of interior opposite angles, We can write ∠COB =∠OPB +∠OBP =2∠OPB So, ∠COB =2∠CPB Similarly, in △POA, OP = OA since both are radii of the circle. So, ∠OPA =∠OAP As the external 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 =2∠APB Substituting, we can get ∠APB =55∘.  Suggest Corrections  0      Similar questions  Related Videos   Recall Arc, Central Angle and Measure of an Arc
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