$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle APB = 130^{\circ}$,then find $\angle ACB$. (in $^{\circ}$)

$AB$ and $CD$ are two chords of a circle with centre $P$. The distance of chord $AB$ from the centre $P$ is $15 \, cm$ and the distance of chord $CD$ from the centre $P$ is $8 \, cm$. If $AB = 16 \, cm$,then find the length of chord $CD$. (in $, cm$)

In a cyclic quadrilateral $PQRS$,$\angle QPR = 40^{\circ}$ and $\angle PSQ = 70^{\circ}$,then find $\angle PQR$. (in $^{\circ}$)

Write True or False and justify your answer in each of the following:
Two congruent circles with centres $O$ and $O^{\prime}$ intersect at two points $A$ and $B$. Then $\angle AOB = \angle AO^{\prime}B$.

State whether each of the following statements is true or false:
$(1)$ $A$ circle divides the plane on which it lies into three parts.
$(2)$ $A$ point,whose distance from the centre of a circle is greater than its radius,lies in the interior of the circle.

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 $, cm$)