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.

Draw a tangent to a given circle with centre $O$ from a point $R$ outside the circle. How many tangents can be drawn to the circle from that point?

Draw a circle with the help of a bangle, take a point outside the circle. Construct the pair of tangents from this point to 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 _____$\mathrm{cm}$.

A triangle $\mathrm{ABC}$ is drawn to circumscribe a circle of radius $3 \mathrm{cm}$ such that $\mathrm{BD}=9 \mathrm{cm}$ and $\mathrm{DC}=3 \mathrm{cm}$. Find the sides $\mathrm{AB}$ and $\mathrm{AC}$.

Two concentric circles are of radii $5 \mathrm{cm}$ and $3 \mathrm{cm}$ are drawn. Find the length (in $\mathrm{cm}$) of the chord of the larger circle which touches the smaller circle.

In the figure, $\mathrm{XY}$ and $\mathrm{X}\text{'}\mathrm{Y}\text{'}$ are two parallel tangents to a circle with centre $\mathrm{O}$ and another tangent $\mathrm{AB}$ with point of contact $\mathrm{C}$ intersecting $\mathrm{XY}$ at $\mathrm{A}$ and $\mathrm{X}\text{'}\mathrm{Y}\text{'}$ at $\mathrm{B}$. Then, $\angle \mathrm{AOB}$ is equal to

If tangents $\mathrm{PA}$ and $\mathrm{PB}$ from a point $\mathrm{P}$ to a circle with centre $\mathrm{O}$ are inclined to each other at angle of $80°$, then $\angle \mathrm{POA}$ is equal to

Prove that the tangents to a circle at the endpoints of a diameter are parallel.

Calculate the length of the tangent from a point $15$ cm away from the centre of a circle of radius $9$ cm.

A tangent $\mathrm{PQ}$ at a point $\mathrm{P}$ of a circle of radius $5$ cm meets a line through the centre $\mathrm{O}$ at a point $\mathrm{Q}$ so that $\mathrm{OQ}=13$ cm. Find the length of $\mathrm{PQ}$.

We can draw _____ tangents to a given circle.

The common point of a tangent to a circle and the circle is called _____ of contact. (point/line)

The number of tangents drawn at the end points of the diameter is _____ .

A tangent to a circle intersects it in _____  point(s).

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.

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