In cyclic quadrilateral $ABCD$,$\angle B = \angle D - 30^{\circ}$,then find $\angle B$. (in $^{\circ}$)

State whether the following statement is True or False and justify your answer: $ABCD$ is a cyclic quadrilateral such that $\angle A = 90^{\circ}, \angle B = 70^{\circ}, \angle C = 95^{\circ}$ and $\angle D = 105^{\circ}$.

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 100^{\circ}$,then find $\angle PCD$. (in $^{\circ}$)

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 $^{\circ}$)

If $ABC$ is an equilateral triangle inscribed in a circle and $P$ is any point on the minor arc $BC$ which does not coincide with $B$ or $C$,prove that $PA$ is the angle bisector of $\angle BPC$.

$AD$ is a diameter of a circle and $AB$ is a chord. If $AD = 34 \, cm$ and $AB = 30 \, cm$,the distance of $AB$ from the centre of the circle is (in $cm$):