Theorems on Tangent to a Circle

Two circles with radii $4 cm$ and $3 cm$ touch each other externally. Find the length of the direct common tangent.

The centres of two circles with radii $6 cm$ and $2 cm$ are $10 cm$ apart. If the length of the transverse common tangent is $k cm$ then the value of $k$ is 

Two circles with radii $25 cm$ and $9 cm$ touch each other externally. Find the length of the direct common tangent.

In the given figure, if two circles touch each other externally at $C$, then prove that the common tangent at $C$ bisects the other two common tangents.

Two circles with radius $17 cm$ and $8 cm$ touch each other. Find the distance between the centres when,

(i) they touch internally

(ii) they touch externally,

Draw a tangent at any point $P$ on the circle having radius $3$ units

The tangent to a circle is a special case of the secant when the two endpoints of corresponding chord coincide

The tangent to a circle is a special case of the secant.

The distance between two parallel tangents to a circle of radius $6 \mathrm{cm}$ is _____ $\mathrm{cm}$.

$O$ 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 intersecting lines of the circle

The number of tangents that can be drawn to a circle from a point inside the circle is _____. (Write the answer in words)

$AB$ is a chord of a circle with centre $O$. The tangent at $B$ meets $AO$ produced at $T$. If $\angle BTA=60°$, find the value of $\angle ABT$. Write the answer in $\mathrm{cm}$.

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.

If a tangent to a circle of radius $3 \mathrm{cm}$ from a point on the concentric circle of radius $4 \mathrm{cm}$ is $\sqrt{k} \mathrm{cm}$, then find the value of $k$.

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

How many tangents can you draw to a circle from a point outside the circle at a fixed distance?

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 $\mathrm{cm}$).

In the following figure, point $‘A’$ is the centre of the circle. Line $MN$ is tangent at point $M$. If $AN=12 \mathrm{cm}$ and $MN=6 \mathrm{cm}$, determine the radius of the circle in $\mathrm{cm}$. $\left(\sqrt{3}=1.73\right)$