Circle and Line

P, Q, R are three point on a circle centre O, XT tangents touch circle at P. If the $\angle TPR={63}^0$ then find the $\angle POR$?

In the given figure, tangents $PQ \& PR$ are drawn to a circle such that$\angle \mathrm{RPQ}=30°$ . A chord $RS$is drawn parallel to $PQ$. Find the $\angle RQS$.

Let $ABCD$ be a circumscribed (or tangential) quadrilateral. Prove that the circles in the two triangles $ABC$ and $ADC$ are tangent to each other.

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 _____ $\mathrm{cm}$.

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

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 _____$\mathrm{cm}$.

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 $\angle AOB=$_____$°$.

A straight line which passes through two points on a circle is

The number of tangents to a circle drawn from a point outside the circle is:

A straight line passing through a point on a circle is

How many tangents can be constructed from a point inside the circle?

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

The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.

In the given figure, $\mathrm{O}$ is the centre of the circle and $\mathrm{AB}=15 \mathrm{cm}$ and $\mathrm{AC}=7.5 \mathrm{cm}$. If the radius of the circle is $r \mathrm{cm}$, then find the value of $r$.

The radius of a circle is $8 \mathrm{cm}$. If the length of a tangent drawn to this circle from a point at a distance of $10 \mathrm{cm}$ from its centre is $k \mathrm{cm}$, then find the value of $k$.