In cyclic quadrilateral $PQRS$,if $5 \angle Q = 7 \angle S$,then find the value of $\angle Q$. (in $^{\circ}$)

$A$ quadrilateral $ABCD$ is inscribed in a circle such that $AB$ is a diameter and $\angle ADC = 130^{\circ}$. Find $\angle BAC$.

The line segment joining the centre and any point on the circle is called a .......... of the circle.

$A$ line joining the midpoints of two chords passes through the centre of a circle. Prove that the chords are parallel.

If circles are drawn taking two sides of a triangle as diameters,prove that the point of intersection of these circles lies on the third side.

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 $AB = 6 \, cm$.