Point $P$ lies in the exterior of a circle with centre $O$. $OP = 34$ and a tangent through $P$ touches the circle at $Q$. If $PQ = 16$,then find the diameter of the circle.

Point $A$ lies in the exterior of $\odot(P, 10)$. $A$ line from $A$ touches the circle at $B$. If $PA = 26$,then find the length of $AB$.

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 $\ldots \ldots \ldots \ldots$.

Radii of two concentric circles are $13$ and $8$. $\overline{AB}$ is a diameter of the circle with the larger radius. $\overline{BD}$ touches the circle with the smaller radius at $D$. Find $AD$.

In the figure,if $PA$ and $PB$ are tangents to the circle with center $O$ such that $\angle APB = 50^{\circ}$,then $\angle OAB$ is equal to: (in $^{\circ}$)

In $\triangle ABC$,$m \angle B = 90^\circ$,$AB = 4$ and $BC = 3$. Find the radius of the incircle of the triangle.