$\overrightarrow{ PA }$ and $\overrightarrow{ PB }$ are tangents to $\odot( O , 5) .$ If $OP = 13,$ then $PB = \ldots \ldots \ldots \ldots$

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 $cm^2$)

Write 'True' or 'False' and give reasons for your answer.
If the angle between two tangents drawn from a point $P$ to a circle of radius $a$ and center $O$ is $90^{\circ}$,then $OP = a\sqrt{2}$.

$A$ line passing through the centre of the circle $O$ intersects the tangent to the circle at $Q$. $P$ is the point of contact. If the radius of the circle is $9$ and $PQ = 40$,then find $OQ$.

In the given figure,if $\angle AOB = 125^{\circ}$,then $\angle COD$ is equal to: (in $^{\circ}$)

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 $RC$.