$\stackrel{\leftrightarrow}{PA}$ and $\stackrel{\leftrightarrow}{PB}$ are tangents to the circle $\odot(O, r)$ at points $A$ and $B$ respectively. If $m\angle OPB = 35^\circ$,then $m\angle AOB = \ldots$ (in $^\circ$)

In the following figure,if $PA = 8$ and $m \angle PAB = 60^\circ$,then the length of $\overline{AB}$ is.......

$A$ circle touches all the sides of $\square ABCD$. If the largest side of $\square ABCD$ is $\overline{AB}$,then the smallest side is:

Write 'True' or 'False' and give reasons for your answer.
$AB$ is a diameter of a circle and $AC$ is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at $C$ intersects $AB$ extended at $D$,then $BC = BD$.

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 $^{\circ}$)

Two circles with centres $O$ and $O^{\prime}$ of radii $3\, cm$ and $4\, cm$,respectively,intersect at two points $P$ and $Q$ such that $OP$ and $O^{\prime}P$ are tangents to the two circles. Find the length of the common chord $PQ$ (in $cm$).