$P$ 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 $r$,if $OP = 30$ and $PY = 24$.

From an external point $P$,two tangents,$PA$ and $PB$ are drawn to a circle with centre $O$. At one point $E$ on the circle,a tangent is drawn which intersects $PA$ and $PB$ at $C$ and $D$,respectively. If $PA = 10 \, cm$,find the perimeter of the triangle $PCD$ (in $cm$).

$P$ 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 $\Delta ABC$,$\angle B = 90^{\circ}$. The radius of the incircle touching all three sides of the triangle is $\ldots \ldots \ldots \ldots$

Two concentric circles have radii $13$ and $8$. $A$ chord of the larger circle touches the smaller circle. Find the length of the chord.

In the figure,$\overrightarrow{ PA }$ and $\overrightarrow{ PB }$ are tangents to $\odot( O , r)$. If $m \angle PAB = 60^{\circ}$,then $m \angle PBA = \ldots$ (in $^{\circ}$)