The line segment joining any two points on a circle is called a ........ of the circle.

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

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. $l$ is the perpendicular bisector of chord $AB$. Prove that $l$ bisects chord $CD$.

In a circle with centre $P$,the distance of a chord $AB$ from the centre $P$ is $20 \, cm$. If $AB = 96 \, cm$,then the radius of the circle is .......... $cm$.

If a line intersects two concentric circles (circles with the same centre) with centre $O$ at $A, B, C$ and $D$,prove that $AB = CD$.

$P$ is the centre of the circle of radius $20\, cm$. $AB$ is a chord of the circle. If $AB = 32\, cm$,then find the distance of the chord $AB$ from the centre $P$.