In the following figure,if $AB = 3$,then the perimeter of $\Delta APQ$ is...........

$\overline{ PA }$ and $\overline{ PB }$ are tangents to the $\odot( O , r)$ drawn from a point $P$ outside the circle,then ..... .

If two circles touch each other externally,then $\ldots \ldots \ldots \ldots$ common tangents can be drawn to them.

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 $^{\circ}$)

Write 'True' or 'False' and give reasons for your answer.
If a chord $AB$ subtends an angle of $60^{\circ}$ at the centre of a circle,then the angle between the tangents at $A$ and $B$ is also $60^{\circ}$.

From an external point $P$,two tangents,$PA$ and $PB$ are drawn to a circle with centre $O$. At one point $E$ on the circle,a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$,respectively. If $PA = 10 \, cm$,find the perimeter of the triangle $PCD$ (in $cm$).