$P$ 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 $m \angle XPO$,if $m \angle XOY = 100^\circ$. (in $^\circ$)

In the following figure,if $PA = 8$ and $m \angle PAB = 60^\circ$,then the length of $\overline{AB}$ is.......

In $\Delta ABC$,$\angle B$ is a right angle. If $AB = 8$ and $BC = 15$,find the radius of the incircle of $\Delta ABC$.

In the figure,if $PQR$ is the tangent to a circle at $Q$ whose center is $O$,$AB$ is a chord parallel to $PR$,and $\angle BQR = 70^{\circ}$,then $\angle AQB$ is equal to: (in $^{\circ}$)

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 $cm$.

In the following figure,if $AB = 15$,then $CD = \ldots$