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 $\ldots \ldots \ldots \ldots$.

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $m \angle XPO$,if $m \angle XOY = 100^\circ$. (in $^\circ$)

Two concentric circles having radii $5$ and $13$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Then the length of the chord is $\ldots \ldots \ldots \ldots.$

$\overline{AB}$ is a chord of $\odot(O, 13)$ such that $AB = 24$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find $PA$.

$\overline{ PA }$ and $\overline{ PB }$ are tangents to the $\odot( O , r)$ drawn from a point $P$ outside the circle,then ..... .

$A$ 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 $OQ$.