$P$ is in the exterior of $\odot (O, 9)$. $A$ tangent from $P$ touches the circle at $T$. If $PT = 40$,then $OP = \ldots$

In the figure,if $O$ is the centre of a circle,$PQ$ is a chord,and the tangent $PR$ at $P$ makes an angle of $50^{\circ}$ with $PQ$,then $\angle POQ$ is equal to: (in $^{\circ}$)

In $\Delta ABC$,if $AB = 7, BC = 24, AC = 25$,then the diameter of a circle touching all the three sides of the triangle is ............

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

$\overline{PA}$ 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 $\ldots \ldots \ldots \ldots .$

$P$ is in the exterior of $\odot(O, 30)$. The tangent drawn from $P$ to the circle touches the circle at $Q$. If $OP = 34$,then $PQ = \dots$