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 $^{\circ}$)

If $\odot(P, r)$ touches all the sides of a quadrilateral $ABCD$,then $ABCD$ is a $\ldots \ldots \ldots \ldots$

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 $cm$.

$AB$ is a diameter and $AC$ is a chord of a circle with centre $O$ such that $\angle BAC = 30^{\circ}$. The tangent at $C$ intersects the extended $AB$ at a point $D$. Prove that $BC = BD$.

Two concentric circles having radii $17$ and $8$ are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

$P$ 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 $m\angle XOP$,if $m\angle XPO = 65^\circ$. (in $^\circ$)