In $\Delta PQR$,$\angle Q$ is a right angle. If $PQ = 8$ and $QR = 15$,then the radius of a circle touching all the three sides of $\Delta PQR$ is $\ldots \ldots.$

For $\Delta ABC$,$a=5$,$b=12$ and $c=13$. The radius of a circle touching all the three sides of $\Delta ABC$ is ..... .

$\overline{PA}$ is a tangent to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $OP = 10$ and $AP = 8$,then the diameter of the circle is equal to $\ldots \ldots \ldots \ldots .$

Two concentric circles have radii $13$ and $8$. $A$ chord of the larger circle touches the smaller circle. Find the length of the chord.

$A$ circle touches all the sides of $\square ABCD$. If the largest side of $\square ABCD$ is $\overline{AB}$,then the smallest side is:

Two concentric circles having radii $41$ and $40$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.