In $\odot(O, 4 \, cm)$,the length of chord $\overline{AB}$ is $4 \, cm$. Then,$m \angle AOB = \ldots$ (in $^\circ$)

Radii of two concentric circles are $13$ and $8$. $\overline{AB}$ is a diameter of the circle with the larger radius. $\overline{BD}$ touches the circle with the smaller radius at $D$. Find $AD$.

Point $P$ lies in the exterior of $\odot(O, r)$. $\overleftrightarrow{PQ}$ touches the circle at $Q$. If $PO = 26$ and $PQ = 10$,then find the diameter of the circle.

Fill in the blanks:
$(i)$ $A$ circle can have $......$ parallel tangents at the most.
$(ii)$ The common point of a tangent to a circle and the circle is called $......$

The length of a tangent from a point $A$ at a distance of $5 \, cm$ from the centre of the circle is $4 \, cm$. Find the radius of the circle. (in $, cm$)

State whether the following statement is 'True' or 'False' and provide reasons for your answer: The length of a tangent from an external point to a circle is always greater than the radius of the circle.