The perpendicular from the centre of a circle to a chord ........... the chord.

$AB$ 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 $CD$.

$A$ line joining the midpoints of two chords passes through the centre of a circle. Prove that the chords are parallel.

Prove that among all the chords of a circle passing through a given point inside the circle,the one that is perpendicular to the diameter passing through the point is the smallest.

In a circle with centre $P$,the diameter of the circle is $70 \, cm$. The chord $AB$ is at a distance of $21 \, cm$ from the centre of the circle,then $AB = \dots \, cm$.

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 $, cm$)