In the figure, there are two concentric circles with centre $\mathrm{O}$. $\mathrm{PRT}$ and $\mathrm{PQS}$ are tangents to the inner circle from a point $\mathrm{P}$ lying on the outer circle. If $\mathrm{P}\mathrm{R}=5 \mathrm{c}\mathrm{m},$ find the length of $\mathrm{PS}$.

In the given figure, $\mathrm{PQ}$ is a tangent from an external point $\mathrm{P}$ to a circle with centre $\mathrm{O}$ and $\mathrm{OP}$ cuts the circle at $\mathrm{T}$ and $\mathrm{QOR}$ is a diameter. If $\mathrm{\angle }\mathrm{P}\mathrm{O}\mathrm{R}=130°$ and $\mathrm{S}$ is a point on the circle, find $\angle 1+\angle 2$ .

In the figure below, $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle from an external point $\mathrm{P}$. $\mathrm{CD}$ is another tangent touching the circle at $\mathrm{Q}$. If $\mathrm{P}\mathrm{A}=12 \mathrm{c}\mathrm{m}, \mathrm{Q}\mathrm{C}=\mathrm{Q}\mathrm{D}=3 \mathrm{c}\mathrm{m},$ then find $\mathrm{P}\mathrm{C}+\mathrm{P}\mathrm{D}$.

In the figure below, $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle drawn from an external point $\mathrm{P}$. $\mathrm{CD}$ is a third tangent touching the circle at $\mathrm{Q}$. If $\mathrm{P}\mathrm{B}=10 \mathrm{c}\mathrm{m}$ and $\mathrm{C}\mathrm{Q}=2 \mathrm{c}\mathrm{m},$ what is the length $\mathrm{PC}$ ?

What is the distance between two parallel tangents of a circle of radius $4 \mathrm{c}\mathrm{m}$?

The length of the tangent from a point $\mathrm{A}$ at a distance of $5 \mathrm{c}\mathrm{m}$ from the centre of the circle is $4 \mathrm{c}\mathrm{m}.$ What is the radius of the circle?

Two tangents $\mathrm{TP}$ and $\mathrm{TQ}$ are drawn from an external point $\mathrm{T}$ to a circle with center $\mathrm{O}$ as shown in the figure. If they are inclined to each other at an angle of $100°$, then what is the value of $\mathrm{\angle }\mathrm{P}\mathrm{O}\mathrm{Q}$?

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What is the distance between two parallel tangents to a circle of radius $5 \mathrm{c}\mathrm{m}$?

In figure, $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle drawn from an external point $\mathrm{P}$. $\mathrm{CD}$ is a third tangent touching the circle at $\mathrm{Q}$. If $\mathrm{PB}=10 \mathrm{cm}$, what is the perimeter of $△\mathrm{P}\mathrm{C}\mathrm{D}?$

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