$A$ tangent to a circle is perpendicular to ..... drawn from the point of contact.

$P$ 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 $PQ = \dots$

Write 'True' or 'False' and give reasons for your answer.
$AB$ is a diameter of a circle and $AC$ is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at $C$ intersects $AB$ extended at $D$,then $BC = BD$.

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

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.

If two tangents inclined at an angle $60^{\circ}$ are drawn to a circle of radius $3 \, cm$,then the length of each tangent is equal to (in $cm$):