Question : In the figure given below, PQ is the diameter of the circle with centre O. If $\angle QOR=100^{\circ}$, then the measure of $\angle PSR$ is:
Option 1: $160^{\circ}$
Option 2: $80^{\circ}$
Option 3: $40^{\circ}$
Option 4: $100^{\circ}$
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Correct Answer: $40^{\circ}$
Solution : Given: $\angle POR = 100^\circ$ Now, POQ is a straight line. ⇒ $\angle POR + \angle QOR = 180^\circ$ ⇒ $100^\circ+\angle POR = 180^\circ$ ⇒ $\angle POR = 180^\circ- 100^\circ = 80^\circ$ Theorem: The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. ⇒ $\angle PSR = \frac{80^\circ}{2} = 40^\circ$ Hence, the correct answer is $40^\circ$.
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Question : In the given figure, the measure of $\angle A$ is:
Option 1: $50^{\circ}$
Option 2: $40^{\circ}$
Option 3: $20^{\circ}$
Option 4: $60^{\circ}$
Question : In the given figure, $\mathrm{O}$ is the centre of the circle and $\angle\mathrm{AOB}=130^{\circ}$. Find $\angle\mathrm{APB}$.
Option 1: $110^{\circ}$
Option 2: $115^{\circ}$
Option 3: $100^{\circ}$
Option 4: $95^{\circ}$
Question : In the given figure, ' $G$ ' is the centre of the circle. Find the $\angle ACB$ when $\angle AGB=132^{\circ}$.
Option 1: $62^{\circ}$
Option 2: $66^{\circ}$
Option 3: $64^{\circ}$
Question : In the given figure, O is the centre of the circle. The circle has 3 tangents. If $\angle QPR=45^{\circ}$, then what is the value (in degrees) of $\angle QOR$?
Option 1: 67.5
Option 2: 72
Option 3: 78.5
Option 4: 65
Question : In the given figure, if $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$ such that $\angle \mathrm{APB}=54^{\circ}$, then $\angle \mathrm{OBA}=$________.
Option 1: 27°
Option 2: 40°
Option 3: 30°
Option 4: 35°
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