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

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.

If a line segment joining the mid-points of two chords of a circle passes through the centre of the circle,prove that the two chords are parallel.

Write True or False and justify your answer.
Two chords of a circle of lengths $10 \, cm$ and $8 \, cm$ are at the distances $8.0 \, cm$ and $3.5 \, cm$,respectively,from the centre.

$ABCD$ is a quadrilateral such that $A$ is the centre of the circle passing through $B, C$ and $D$. Prove that $\angle CBD + \angle CDB = \frac{1}{2} \angle BAD$.

In a cyclic quadrilateral $ABCD$,$\angle A = 2x - 10^{\circ}$ and $\angle C = 3x - 35^{\circ}$,then $\angle A =$ .......... (in $^{\circ}$)