In a circle with centre $P$,$AB$ and $CD$ are chords. If $\angle APB = 80^{\circ}$,$\angle CPD = 50^{\circ}$ and $AB = 7\, cm$,then find the length of chord $CD$. (in $, cm$)

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 70^{\circ}$,then find $\angle CPD$. (in $^{\circ}$)

Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.

In the figure,$\angle PQR = 100^{\circ}$,where $P, Q$ and $R$ are points on a circle with centre $O$. Find $\angle OPR$. (in $^{\circ}$)

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

$AB$ is a chord of a circle with centre $P$. Point $C$ is a point other than $A$ and $B$ on the major arc $AB$. If $\angle ACB + \angle APB = 135^{\circ}$,then find $\angle ACB$ and $\angle APB$.