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 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: $100^{\circ}$

Question : In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of $\angle {AQR}$ and $\angle {BRQ}$ intersect at point O. If $\angle {QOR} = 50^{\circ}$ what is the value of $\angle {QPR}$ ?

Option 1: $50^{\circ}$

Option 2: $60^{\circ}$

Option 3: $80^{\circ}$

Option 4: $100^{\circ}$

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, 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°

Question : PQ is a tangent of a circle at T. If TR = TS where R and S are points on the circle and $\angle RST=65^{\circ}$, the $\angle PTS=?$

Option 1: $65^{\circ}$

Option 2: $130^{\circ}$

Option 3: $115^{\circ}$

Option 4: $55^{\circ}$