$P$ 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 $^\circ$)

In the figure,$\stackrel{\leftrightarrow}{ AB }$,$\stackrel{\leftrightarrow}{ AC }$ and $\stackrel{\leftrightarrow}{ PQ }$ are tangents to $\odot( O , r)$. If the perimeter of $\Delta APQ$ is $16$,then $AB = \ldots$

$\overline{PA}$ is a tangent to $\odot(O, 8)$ drawn from a point $P$ outside the circle. If $m\angle AOP = 45^\circ$,then $AP = \ldots$

Write 'True' or 'False' and give reasons for your answer.
The angle between two tangents to a circle may be $0^{\circ}$.

$\odot(O, 41)$ and $\odot(O, 9)$ are concentric circles. The chord $\overline{AB}$ of $\odot(O, 41)$ touches $\odot(O, 9)$ at point $M$. Then $AB = \ldots$

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.