$A$ tangent to a circle forms an angle of measure $\ldots \ldots \ldots \ldots$ with the radius drawn at the point of contact. (in $^{\circ}$)

Write 'True' or 'False' and give reasons for your answer.
If a number of circles touch a given line segment $PQ$ at a point $A$,then their centres lie on the perpendicular bisector of $PQ$.

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 $^{\circ}$)

$P$ 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 $OP$,if $r = 12$ and $XP = 5$.

Point $A$ lies in the exterior of $\odot(P, 10)$. $A$ line from $A$ touches the circle at $B$. If $PA = 26$,then find the length of $AB$.

$P$ is in the exterior of $\odot(O, 30)$. The tangent drawn from $P$ to the circle touches the circle at $Q$. If $OP = 34$,then $PQ = \dots$