VERY SHORT ANSWER TYPE QUESTIONS (VSAQs)

In figure, $\mathrm{CP}$ and $\mathrm{CQ}$ are tangents to a circle with centre $\mathrm{O}$. $\mathrm{ARB}$ is another tangent touching the circle at $\mathrm{R}$. If $\mathrm{C}\mathrm{P}=11 \mathrm{c}\mathrm{m}$ and $\mathrm{B}\mathrm{C}=7 \mathrm{c}\mathrm{m},$ then find the length of $\mathrm{BR}$.

In figure, $△\mathrm{ABC}$ is circumscribing a circle. Find the length of $\mathrm{BC}$.

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In, figure, $\mathrm{CP}$ and $\mathrm{CQ}$ are tangents from an external point $\mathrm{C}$ to a circle with centre $\mathrm{O}$. $\mathrm{AB}$ is another tangent which touches the circle at $\mathrm{R}$. If $\mathrm{CP}=11 \mathrm{cm}$ and $\mathrm{BR}=4 \mathrm{cm}$, if the length of $\mathrm{BC}=k\mathit{ }\mathrm{cm}$, find $k$.

Two concentric circles are of radii $5 \mathrm{c}\mathrm{m}$ and $3 \mathrm{c}\mathrm{m}.$ Find the length of the chord of the larger circle which touches the smaller circle.

In figure, $PA$ and $PB$ are tangent to the circle with centre $\mathrm{O}$ such that $\angle APB=50°$. If the measure of $\angle \mathrm{OAB} =k°$, find $k$.

In figure, $\mathrm{PQ}$ is a chord of a circle and $\mathrm{PT}$ is the tangent at $\mathrm{P}$ such that $\mathrm{\angle }\mathrm{Q}\mathrm{P}\mathrm{T}=60°.$ Then, find $\mathrm{\angle }\mathrm{P}\mathrm{R}\mathrm{Q}\mathrm{}.$

In figure, $\mathrm{PQL}$ and $\mathrm{PRM}$ are tangents to the circle with centre $\mathrm{O}$ at the points $\mathrm{Q}$ and $\mathrm{R}$ respectively and $\mathrm{S}$ is a point on the circle such that $\angle \mathrm{S}\mathrm{Q}\mathrm{L}=50°$and $\angle \mathrm{S}\mathrm{R}\mathrm{M}=60°.$ Then, find $\angle \mathrm{Q}\mathrm{S}\mathrm{R}.$

In the given figure, $\mathrm{BOA}$ is a diameter of a circle and the tangent at a point $\mathrm{P}$ meets $\mathrm{BA}$ produced at $\mathrm{T}$. If $\mathrm{}\mathrm{\angle }\mathrm{P}\mathrm{B}\mathrm{O}=30°$, then find $\mathrm{\angle }\mathrm{P}\mathrm{T}\mathrm{A}$.