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 length of a tangent from a point $A$ at distance $5$ cm from the centre of the circle is $4$ cm. Find the radius of the circle.

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

From a point $Q$, the length of the tangent to a circle is $24$ cm and the distance of $Q$ from the centre is $25$ cm. The radius of the circle is-

A triangle $ABC$ is drawn to circumscribe a circle of radius $4cm$  such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of the lengths $8cm$ and $6cm$ respectively. Find the sides $AB$ and $AC$.

In Figure  If $TP$ and $TQ$ are the two tangents to a circle with centre $O$ so that $\angle POQ$ $=110^o$, the $\angle$ $PTQ$ is equal to.

Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.

How many tangents can a circle have?

Prove that the parallelogram circumscribing a circle is a rhombus.