Tangent to a Circle

In a park, four poles are standing at positions $A, B, C$ and $D$ around the fountain such that the cloth joining the poles $AB, BC. CD$ and $DA$ touches the fountain at $P, Q, R$ and $S$ respectively as shown in figure:

Based on the above information, answer the following question:

If $O$ is the centre of the circular fountain, then $\angle OSA=$

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.

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

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 $25 \mathrm{cm}$. The radius of the 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 $\mathrm{cm}$.

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

A circle with centre at $\text{'}O\text{'}$ touches the four sides of a quadrilateral $ABCD$ internally in such a way that it divides $AB$ in $3:1$ and $AB= 8 \mathrm{cm}$. If the radius of the circle is $x \mathrm{cm}$, where $OA = 10 \mathrm{cm}$, find the value of $x$.

Two parallel lines touch the circle at points $\mathrm{A}$ and $\mathrm{B}$, respectively. If area of the circle is$25\pi {\mathrm{cm}}^2$, then $\mathrm{AB}$ is equal to

$\mathrm{ABCD}$ is a cyclic quadrilateral and $\mathrm{PQ}$ is a tangent to the circle at $C$. If $\mathrm{BD}$ is a diameter, $\angle DCQ=40°$ and $\angle ABD=60°$ then find the measure of $\angle \mathrm{ADB}$ (write answer without degree symbol) is

$\mathrm{ABCD}$ is a cyclic quadrilateral and $\mathrm{PQ}$ is a tangent to the circle at $C$.  If $\mathrm{BD}$ is a diameter, $\angle DCQ=40°$ and $\angle ABD=60°$,  the measure of $\angle \mathrm{BCP}=k°$. Then find the value of $k$

To draw a pair of tangents to a circle which are inclined to each other at an angle of $60°$, it is required to draw tangents at the end points of those two radii of the circle. If the angle between them is $x°$, then the value of $x$ is

The point at which a tangent is perpendicular to the radius is called point of _____ (centre, tangency, radius)