If the measure of the angle between two radii of the circle is $48^{\circ}$,then the measure of the angle between the tangents drawn at the end points of the radii is $\ldots \ldots \ldots$ (in $^{\circ}$)

In the figure,common tangents $AB$ and $CD$ to two circles intersect at $E$. Prove that $AB = CD$.

$P$ lies in the exterior of $\odot(O, 8)$ such that $OP = 17$. Two tangents are drawn to the circle which touch the circle at $A$ and $B$. Find $AB$.

$A$ is a point at a distance $13\, cm$ from the centre $O$ of a circle of radius $5 \,cm$. $AP$ and $AQ$ are the tangents to the circle at $P$ and $Q$. If a tangent $BC$ is drawn at a point $R$ lying on the minor arc $PQ$ to intersect $AP$ at $B$ and $AQ$ at $C$,find the perimeter of the $\triangle ABC$. (in $cm$)

How many tangents can a circle have?

In the figure,$\overrightarrow{ PA }$ and $\overrightarrow{ PB }$ are tangents to $\odot( O , r)$. If $m \angle PAB = 60^{\circ}$,then $m \angle PBA = \ldots$ (in $^{\circ}$)