$AB$ is a diameter of a circle. $l_{1}$ and $l_{2}$ are tangents to the circle drawn at points $A$ and $B$ respectively. Then,which of the following is true?

$A$ circle with centre $O$ touches sides $\overline{AB}$,$\overline{BC}$,$\overline{CD}$ and $\overline{DA}$ of quadrilateral $ABCD$ at points $P, Q, R$ and $S$ respectively. Prove that $m \angle AOB + m \angle COD = 180^{\circ}$ and $m \angle AOD + m \angle BOC = 180^{\circ}$.

$\overline{AB}$ is a chord of $\odot(O, 10)$ such that $AB = 16$. Tangents at $A$ and $B$ to the circle intersect at $P$. Find the length of $PA$.

$A$ circle touches all four sides of $\square ABCD$. If $AB = 5, BC = 8$ and $CD = 6$,then $AD = .......$

In the given figure,$AT$ is a tangent to the circle with center $O$ such that $OT = 4 \, cm$ and $\angle OTA = 30^{\circ}$. Then $AT$ is equal to (in $cm$):

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 $^{\circ}$)