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

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 $40^{\circ}$.

Two concentric circles having radii $17$ and $8$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

Prove that a diameter $AB$ of a circle bisects all those chords which are parallel to the tangent at the point $A$.

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

If $\odot(P, r)$ touches all the sides of a quadrilateral $ABCD$,then $ABCD$ is a $\ldots \ldots \ldots \ldots$