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

$A$ tangent to a circle intersects the circle in $\ldots \ldots \ldots .$

In $\Delta ABC$,$\angle B = 90^{\circ}$. The radius of the incircle touching all three sides of the triangle is $\ldots \ldots \ldots \ldots$

$A$ circle touches all the sides of a quadrilateral $ABCD$. If $AB = 8$,$BC = 10$,and $CD = 7$,then find the length of $AD$.

$A$ 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 $cm$)

$\odot(O, 41)$ and $\odot(O, 9)$ are concentric circles. The chord $\overline{AB}$ of $\odot(O, 41)$ touches $\odot(O, 9)$ at point $M$. Then $AB = \ldots$