In the figure,the pair of tangents $AP$ and $AQ$ drawn from an external point $A$ to a circle with centre $O$ are perpendicular to each other and the length of each tangent is $5 \, cm$. Then the radius of the circle is (in $cm$):

$\stackrel{\leftrightarrow}{PA}$ 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 $^\circ$)

$A$ line drawn from the centre $O$ of a circle with radius $7 \, cm$ intersects the tangent at point $P$ on the circle at point $Q$,such that $PQ = 24 \, cm$. Find $OQ$.

Two tangents $PQ$ and $PR$ are drawn from an external point $P$ to a circle with centre $O$. Prove that $QORP$ is a cyclic quadrilateral.

$A$ circle with centre $O$ touches sides $\overline{AB}$,$\overline{BC}$,$\overline{CD}$ and $\overline{DA}$ of quadrilateral $ABCD$ at points $P, Q, R$ and $S$ respectively. Prove that $m \angle AOB + m \angle COD = 180^{\circ}$ and $m \angle AOD + m \angle BOC = 180^{\circ}$.

In the figure,$O$ is the centre of a circle of radius $5 \, cm$. $T$ is a point such that $OT = 13 \, cm$ and $OT$ intersects the circle at $E$. If $AB$ is the tangent to the circle at $E$,find the length of $AB$ in $cm$.