If the angle between two radii of a circle is $130^{\circ}$,the angle between the tangents at the ends of the radii is: (in $^{\circ}$)

$\overline{AB}$ is a chord of a circle with centre $O$. Line $l$ touches the circle at $B$. The foot of the perpendicular from $A$ to $l$ is $D$. Prove that $\angle BAO \cong \angle BAD$.

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 $cm$).

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

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