$A$ tangent to a circle intersects the circle in $\ldots \ldots \ldots .$

$\overline{AB}$ 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 $\angle BAO \cong \angle BAD$.

In the following figure,if $PA = 8$ and $m \angle PAB = 60^\circ$,then the length of $\overline{AB}$ is.......

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.

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.

If $ABCD$ is a cyclic quadrilateral and $m \angle B = 60^{\circ}$,then the measure of $\angle D = \dots$ (in $^{\circ}$)