In the given figure,if $\angle AOB = 125^{\circ}$,then $\angle COD$ is equal to: (in $^{\circ}$)

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 $\Delta ABC$,$m \angle B = 90^{\circ}$. $A$ circle touches all the sides of $\Delta ABC$. If $AB + AC = 32$ and $BC = 24$,then find the radius of the incircle.

In $Fig.$,$PQ$ is a chord of a circle and $PT$ is the tangent at $P$ such that $\angle QPT = 60^{\circ}$. Then $\angle PRQ$ is equal to (in $^{\circ}$)

$A$ is a point at a distance $13\, cm$ from the centre $O$ of a circle of radius $5 \,cm$. $AP$ and $AQ$ are the tangents to the circle at $P$ and $Q$. If a tangent $BC$ is drawn at a point $R$ lying on the minor arc $PQ$ to intersect $AP$ at $B$ and $AQ$ at $C$,find the perimeter of the $\triangle ABC$. (in $cm$)

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 $AB$ ..... .