Question : AB is the diameter of a circle with centre O. P is a point on the circle. If $\angle AOP=95^{\circ}$, then $\angle{OBP}=$
Option 1: $57.5^{\circ}$
Option 2: $45.5^{\circ}$
Option 3: $47.5^{\circ}$
Option 4: $55.5^{\circ}$
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Correct Answer: $47.5^{\circ}$
Solution :
Given: AB is the diameter of a circle with centre O.
P is a point on it.
As we know, the angle subtended by an arc at the centre is twice the angle subtended by the same arc on the circle.
$\angle AOP= 2\angle ABP$
⇒ $95^{\circ} = 2\angle ABP$
⇒ $\angle ABP= \frac{95^{\circ}}{2}$
⇒ $\angle OBP= 47.5^{\circ}$
Hence, the correct answer is $47.5^{\circ}$.
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