If $\odot(O, 5)$ touches all the sides of a square,then the perimeter of the square is .... .

$A$ circle touches all the sides of $\square ABCD$. If the largest side of $\square ABCD$ is $\overline{AB}$,then the smallest side is:

Let $P$ be the centre of a circle and $AB$ be a line in the same plane. If $Q$ is the foot of the perpendicular drawn from $P$ to the line $AB$,and $Q$ lies in the interior of the circle,then the line $AB$ ..... .

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 $BD = s - b$.

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

If the angle between two radii of a circle is $130^{\circ}$,the angle between the tangents at the ends of the radii is: (in $^{\circ}$)