In a circle with centre $P$,$AB$ is a chord. If the length of a radius is $17\,cm$ and $AB = 30\,cm$,then find the distance of $AB$ from the centre $P$. (in $,cm$)

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 the figure,if $OA = 5 \text{ cm}$,$AB = 8 \text{ cm}$,and $OD$ is perpendicular to $AB$,then $CD$ is equal to (in $\text{cm}$):

In a circle with centre $P$,the length of chord $AB$ is $40 \, cm$. $AB$ lies at a distance of $21 \, cm$ from the centre $P$. Find the diameter of the circle. (in $, cm$)

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

$AB$ and $XY$ are two chords of a circle whose centre is $P$. $A$ line $l$ passing through the centre $P$ bisects chords $AB$ and $XY$ both. Prove that $AB \parallel XY$.