Point $A$ lies in the exterior of $\odot(O, 8)$. $A$ line through $A$ touches the circle at $B$. If $AB = 15$,then find $OA$.

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 $^{\circ}$)

$\odot(O, 17)$ and $\odot(O, 15)$ are concentric circles. The chord $\overline{AB}$ of $\odot(O, 17)$ touches $\odot(O, 15)$. Then $AB = \ldots$

Write 'True' or 'False' and give reasons for your answer.
In the figure,$PQL$ and $PRM$ are tangents to the circle with center $O$ at the points $Q$ and $R$ respectively,and $S$ is a point on the circle such that $\angle SQL = 50^{\circ}$ and $\angle SRM = 60^{\circ}$. Then $\angle QSR$ is equal to $40^{\circ}$.

$A$ circle touches the sides $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ of $\Delta ABC$ at the points $D, E, F$ respectively. If $AB=13$,$BC=12$,and $CA=5$,then $AD = \ldots$

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