Tangent to a Circle

If$AP=12 cm, OP=13 cm$, then $CD=?$

$O$ is the centre of the circle  in the figure. $\mathrm{PQ}$ is the tangent to the circle and $\mathrm{P}$ is the tangent point of contact. What is the value of $\angle \mathrm{OPQ}$?

$O$ is the center of the circle in the figure, and some line segments have been drawn. Find the two tangents to the circle

The distance of a point $P$ lying outside of a circle from the centre of that circle is $10 \mathrm{cm}$. If the length of the tangent of the circle drawn from $P$ is $8 \mathrm{cm}$, then find the diameter (in cm) of the circle.

In the figure, if $AD=15 \mathrm{cm}, CF=12 \mathrm{cm}$ and $BE=7 \mathrm{cm}$, then the perimeter of the triangle $ABC$ is _____$\mathrm{cm}$.

The angle between a tangent to a circle and the radius drawn at the point of contact is

In the given figure $PQ$ and $RS$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersecting $PQ$ at $A$ and $RS$ at $B$. Then $\angle AOB=$_____$°$.

The length of the tangent to a circle from a point $17 \mathrm{cm}$ from its centre is $8 \mathrm{cm}$. Find the radius of the circle (in $\mathrm{cm}$).

A point $P$ is $25 \mathrm{cm}$ from the centre $O$ of the circle. The length of the tangent drawn from $P$ to the circle is $24 \mathrm{cm}$. Find the radius of the circle (in $\mathrm{cm}$).

A straight line passing through a point on a circle is

From a point $Q$ the length of the tangent to a circle is $24 \mathrm{cm}$ and the distance of $Q$ from the centre is $25 \mathrm{cm}$. Find the radius of circle in $\mathrm{cm}$.

A circle with centre $O$ touches all the four sides of a quadrilateral $ABCD$ internally in such a way that it divides $AB$ in $3:1$ and $AB=12 \mathrm{cm}$, then find the radius of circle where $OA=15\mathrm{cm}$.

In the given figure, find $\mathrm{TP}$ if $\mathrm{AT}=16\mathrm{cm}$ and $\mathrm{AB}=12\mathrm{cm}.$ (in $\mathrm{cm}$)

In the following figure, $\mathrm{PQ}$ and $\mathrm{PR}$ are tangents to the circle, with centre $\mathrm{O}.$ If $\angle \mathrm{QPR} = 60°,$ calculate $\angle \mathrm{QOR}.$

In a triangle $\mathrm{ABC},$ the incircle with centre $\mathrm{O}$ touches $\mathrm{BC}, \mathrm{CA}$and $\mathrm{AB}$ at points $\mathrm{P},$ $\mathrm{Q}$ and $\mathrm{R}$ respectively. Calculate $\angle \mathrm{QOR}$, given that $\angle \mathrm{A} = 60°.$

In the following figure, $\mathrm{PQ}$ is the tangent to the circle at $\mathrm{A}, \mathrm{DB}$ is the diameter and $\mathrm{O}$ is the centre of the circle. If $\angle \mathrm{ADB} = 30°$ and $\angle \mathrm{CBD} = 60°,$ calculate $\angle \mathrm{PAD}.$

The given figure shows a circle with centre $\mathrm{O}$ and $\mathrm{BCD}$ is tangent to it at $\mathrm{C}.$ Show that $\angle \mathrm{ACD}+\angle \mathrm{BAC}=90°.$

In the given figure, $\mathrm{MN}$ is the common chord of two intersecting circles and $\mathrm{AB}$ is their common tangent. Prove that the line $\mathrm{NM}$ produced bisects $\mathrm{AB}$ at $\mathrm{P}.$

In two concentric circles, prove that all chords of the outer circle, which touch the inner circle, are of equal length.

Two parallel tangents of a circle meet a third tangent at points $\mathrm{P}$ and $\mathrm{Q}.$ Prove that $\mathrm{PQ}$ subtends a right angle at the centre.