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

Prove that the quadrilateral formed (if possible) by the internal angle bisectors of any quadrilateral is cyclic.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides,prove that the quadrilateral so formed is cyclic.

In a cyclic quadrilateral $ABCD$,diagonals $AC$ and $BD$ intersect at $P$. If $\angle BAC = 52^{\circ}$ and $\angle ADB = 78^{\circ}$,then find $\angle ABC$. (in $^{\circ}$)

In a cyclic quadrilateral $PQRS$,$\angle P = \angle R + 50^{\circ}$. Find $\angle P$ and $\angle R$.

If $BM$ and $CN$ are the perpendiculars drawn on the sides $AC$ and $AB$ of the triangle $ABC$,prove that the points $B, C, M$ and $N$ are concyclic.