In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 80^{\circ},$ then $\angle CPD =$ .......... (in $^{\circ}$)

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 $\angle ACB + \angle APB = 150^{\circ}$,then find $\angle APB$. (in $^{\circ}$)

The perpendicular from the centre of a circle to a chord ........... the chord.

$AB$ and $AC$ are two chords of a circle with centre $P$. If the bisector of $\angle BAC$ passes through the centre $P$,prove that $AB = AC$.

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 $ABCD$,$\angle A = 4 \angle C$ and $\angle B = 3 \angle D$. Find all the angles of $ABCD$.