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

The chord of $\odot(O, 34)$ touches $\odot(O, 16)$. The length of the chord 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:

$A$ 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 $m \angle AOD + m \angle BOC = 180^{\circ}$.

$P$ is a point in the exterior of $\odot(O, r)$ and the tangents from $P$ to the circle touch the circle at $X$ and $Y$. Find $OP$,if $r = 12$ and $XP = 5$.

State whether the following statement is 'True' or 'False' and provide reasons for your answer: The length of a tangent from an external point to a circle is always greater than the radius of the circle.