In a circle with centre $O$,two chords $PQ$ and $RS$ subtend equal angles at the centre. If $PQ = 12 \text{ cm}$,then $RS = \dots \text{ cm}$.

In the figure,$\angle ACB = 40^{\circ}$. Find $\angle OAB$.

In a circle with centre $P$,the chord $AB = 8 \, cm$ and the radius $= 8 \, cm$. Then,$\angle APB = \dots$ (in $^{\circ}$)

Write True or False and justify your answer in each of the following:
$A$ circle of radius $3 \, cm$ can be drawn through two points $A$ and $B$ such that $AB = 6 \, cm$.

In a circle with centre $O$,$PQ$ and $RS$ are chords. If $\angle POQ = 90^{\circ}$,$\angle ROS = 90^{\circ}$ and $PQ = 6\, cm$,then $RS = \dots \, cm$.

In a circle with centre $P$,the radius is $13 \, cm$. The distance between two parallel chords $AB$ and $CD$ is $17 \, cm$. If $AB = 24 \, cm$,find the length of $CD$. (in $, cm$)