$\overline{PA}$ and $\overline{PB}$ are the tangents to $\odot(O, r)$ drawn from a point $P$ outside a circle. If $m \angle APB = 70^\circ$,then $m \angle POB = \dots$ (in $^\circ$)

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

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

At one end $A$ of a diameter $AB$ of a circle of radius $5 \, cm$,a tangent $XY$ is drawn to the circle. The length of the chord $CD$ parallel to $XY$ and at a distance of $8 \, cm$ from $A$ is (in $cm$):

In the figure,the common tangents $AB$ and $CD$ to two circles with centers $O$ and $O^{\prime}$ intersect at $E$. Prove that the points $O, E, O^{\prime}$ are collinear.

In the figure,$AB$ is a chord of the circle and $AOC$ is its diameter such that $\angle ACB = 50^{\circ}$. If $AT$ is the tangent to the circle at point $A$,then $\angle BAT$ is equal to (in $^{\circ}$)