As shown in the figure,$AB$,$AC$ and $\overleftrightarrow{PQ}$ are tangents to the circle. If $AB = 6$,then the perimeter of $\Delta APQ = \ldots \ldots \ldots$.

Write 'True' or 'False' and give reasons for your answer.
The angle between two tangents to a circle may be $0^{\circ}$.

If tangents $PA$ and $PB$ from a point $P$ to a circle with centre $O$ are inclined to each other at an angle of $80^{\circ}$,then $\angle POA$ is equal to ......$^{\circ}$

In the figure,the pair of tangents $AP$ and $AQ$ drawn from an external point $A$ to a circle with centre $O$ are perpendicular to each other and the length of each tangent is $5 \, cm$. Then the radius of the circle is (in $cm$):

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.

If $a, b, c$ are the sides of a right triangle where $c$ is the hypotenuse,prove that the radius $r$ of the incircle of the triangle is given by $r = \frac{a + b - c}{2}$.