In a circle with radius $17 \, cm$,the length of a chord is $30 \, cm$. Find the distance of the chord from the centre. (in $, cm$)

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 the perpendicular bisector of a chord $AB$ of a circle $PXAQBY$ intersects the circle at $P$ and $Q$,prove that arc $PXA \cong$ arc $PYB$.

Two circles with centres $O$ and $O'$ intersect at two points $A$ and $B$. $A$ line $PQ$ is drawn parallel to $OO'$ through $A$ (or $B$) intersecting the circles at $P$ and $Q$. Prove that $PQ = 2 OO'$.

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 $P$. Centre $P$ is not between the two chords $AB$ and $CD$. If $AB = 40\,cm$,$CD = 30\,cm$ and the radius of the circle is $25\,cm$,find the distance between $AB$ and $CD$. (in $,cm$)