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

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 the figure,tangents $PQ$ and $PR$ are drawn to a circle such that $\angle RPQ = 30^{\circ}$. $A$ chord $RS$ is drawn parallel to the tangent $PQ$. Find the $\angle RQS$. (in $^{\circ}$)

In $\Delta ABC$,$\angle B$ is a right angle. If $AB = 8$ and $BC = 6$,find the radius of the incircle of $\Delta ABC$.

State whether the following statement is 'True' or 'False' and provide reasons for your answer: The length of a tangent from an external point to a circle is always greater than the radius of the circle.

$\overline{AB}$ is a chord of a circle with centre $O$. Line $l$ touches the circle at $B$. The foot of the perpendicular from $A$ to $l$ is $D$. Prove that $\angle BAO \cong \angle BAD$.