The diagram shows a circle , centre $O$. The line $PS$ is a tangent to the circle. Calculate angle $PQS$.

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

In the following figure, point ‘$A$’ is the centre of the circle. Line $MN$ is tangent at point $M$. If $AN=10 \mathrm{cm}$ and $MN=6 \mathrm{cm}$, determine the radius of the circle.

In given figure, if $\mathrm{TP} \mathrm{and} \mathrm{TQ}$ are the two tangents to a circle with centre $O$ so that $\angle POQ=110°$, find angle $\angle PTQ$.

Prove that, “the lengths of the two tangent segments to a circle drawn from an external point are equal”.