In cyclic quadrilateral $PQRS$,if $\angle PRQ = 52^{\circ}$,then find $\angle PSQ$. (in $^{\circ}$)

In the figure,if $\angle OAB = 40^{\circ},$ then $\angle ACB$ is equal to: (in $^{\circ}$)

$A$ point located in the plane of a circle and which is equidistant from every point on the circle is called the ........ of the circle.

In the given figure,if $\angle BCD = 40^{\circ}$ and $\angle BAE = 65^{\circ},$ then find the values of $a, b,$ $c$ and $d$.

Prove that two circles cannot intersect at more than two points.

In a circle with centre $P$,$AB$ is a chord and point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB = 47^{\circ},$ then $\angle APB = $ .......... (in $^{\circ}$)