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.
In the figure,$PQL$ and $PRM$ are tangents to the circle with center $O$ at the points $Q$ and $R$ respectively,and $S$ is a point on the circle such that $\angle SQL = 50^{\circ}$ and $\angle SRM = 60^{\circ}$. Then $\angle QSR$ is equal to $40^{\circ}$.

Write 'True' or 'False' and give reasons for your answer.
In the figure,$BOA$ is a diameter of a circle and the tangent at a point $P$ meets $BA$ extended at $T$. If $\angle PBO = 30^{\circ}$,then $\angle PTA$ is equal to $30^{\circ}$.

In the figure,tangents $PQ$ and $PR$ are drawn to a circle such that $\angle RPQ = 30^{\circ}$. $A$ chord $RS$ is drawn parallel to the tangent $PQ$. Find the $\angle RQS$. (in $^{\circ}$)

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 $AB$ ..... .

In the figure,$O$ is the centre of a circle of radius $5 \, cm$. $T$ is a point such that $OT = 13 \, cm$ and $OT$ intersects the circle at $E$. If $AB$ is the tangent to the circle at $E$,find the length of $AB$ in $cm$.