In $\Delta ABC$,$\angle B$ is a right angle. If $AB = 24$ and $BC = 7$,then the radius of the circle touching all three sides of $\Delta ABC$ is $\ldots \ldots \ldots \ldots$.

From a point $P$ which is at a distance of $13 \, cm$ from the centre $O$ of a circle of radius $5 \, cm$,the pair of tangents $PQ$ and $PR$ to the circle are drawn. Then the area of the quadrilateral $PQOR$ is (in $cm^2$)

The incircle of $\Delta ABC$ touches the sides $\overline{AB}$, $\overline{BC}$ and $\overline{CA}$ at points $P$, $Q$ and $R$ respectively. If $AB = 14$, $BC = 11$ and $CA = 7$, find the lengths of $AP$, $BQ$ and $RC$.

$\overline{AB}$ is a diameter of $\odot(O, 15)$. $A$ tangent is drawn from $B$ to $\odot(O, 9)$ which touches $\odot(O, 9)$ at $D$. $\overrightarrow{BD}$ intersects $\odot(O, 15)$ at $C$. Find $AC$.

$\square PQRS$ is a cyclic quadrilateral. If $m \angle P = 30^{\circ}$, then $m \angle R = \dots$ (in $^{\circ}$)

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 $^{\circ}$)