How many tangents can a circle have?

$\overline{ PA }$ and $\overline{ PB }$ are the tangents to $\odot( O , r)$ drawn from a point $P$ outside a circle. If $m \angle APB = 65^{\circ}$,then $m \angle AOB = \ldots \ldots \ldots . .$ (in $^{\circ}$)

Let $s$ denote the semi-perimeter of a triangle $ABC$ in which $BC = a, CA = b, AB = c$. If a circle touches the sides $BC, CA, AB$ at $D, E, F$ respectively,prove that $BD = s - b$.

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

Write True or False and give reasons for your answer.
$A$ pair of tangents can be constructed from a point $P$ to a circle of radius $3.5 \, cm$ situated at a distance of $3 \, cm$ from the centre.

$\overline{AB}$ is a chord of $\odot(O, 10)$ such that $AB = 16$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find the length of $PA$.