In the figure,if $\angle ABC = 20^{\circ},$ then $\angle AOC$ is equal to (in $^{\circ}$)

In the figure,if $AOB$ is a diameter of the circle and $AC = BC$,then $\angle CAB$ is equal to (in $^{\circ}$)

In a circle with centre $P$,the chord $AB = 8 \, cm$ and the radius $= 8 \, cm$. Then,$\angle APB = \dots$ (in $^{\circ}$)

Prove that if chords of congruent circles subtend equal angles at their centres,then the chords are equal.

In a circle with centre $P$,$AB$ is a diameter and point $C$ is a point other than $A$ and $B$. If the radius of the circle is $34 \, cm$ and $AC = 32 \, cm$,then $BC = $ .......... $cm$.

Two circles of radii $8 \ cm$ with centers $P$ and $Q$ are given. The chord $AB$ of the circle with center $P$ and the chord $CD$ of the circle with center $Q$ are equal. If $\angle PAB = 40^{\circ}$,then find $\angle CQD$. (in $^{\circ}$)