The longest chord of a circle is a .......... of the circle.

In a circle with centre $O$,$PQ$ and $RS$ are chords. If $\angle POQ = 90^{\circ}$,$\angle ROS = 90^{\circ}$ and $PQ = 6\, cm$,then $RS = \dots \, cm$.

Write True or False and justify your answer in each of the following: Two chords $AB$ and $CD$ of a circle are each at distances $4 \ cm$ from the centre. Then $AB = CD$.

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

In the figure,$OD$ is perpendicular to chord $AB$ of a circle whose centre is $O.$ If $BC$ is a diameter,prove that $CA = 2OD$.

In the figure,if $\angle DAB = 60^{\circ}$ and $\angle ABD = 50^{\circ}$,then $\angle ACB$ is equal to: (in $^{\circ}$)