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

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,$AB$ 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 $^{\circ}$)

$A$ tangent to a circle is perpendicular to ..... drawn from the point of contact.

Radii of two concentric circles are $13$ and $8$. $\overline{AB}$ is a diameter of the circle with the larger radius. $\overline{BD}$ touches the circle with the smaller radius at $D$. Find $AD$.

In $\Delta ABC$,$\angle B$ is a right angle. If $AB = 24$ and $BC = 7$,then the radius of the circle touching all three sides of $\Delta ABC$ is $\ldots \ldots \ldots \ldots$.