$P$ 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 $P$.

The radius of a circle with centre $P$ is $50 \, cm$. Centre $P$ is not lying between two parallel chords $AB$ and $CD$. If $AB = 80 \, cm$ and the distance between $AB$ and $CD$ is $10 \, cm$,then find the length of $CD$. (Given $AB > CD$) (in $, cm$)

In the figure,if $\angle OAB = 40^{\circ},$ then $\angle ACB$ is equal to: (in $^{\circ}$)

$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between the chords $AB$ and $CD$. If $AB = 20\,cm$,$CD = 48\,cm$,and the radius of the circle is $26\,cm$,find the distance between $AB$ and $CD$.

$ABCD$ is a parallelogram. $A$ circle through $A$ and $B$ is drawn such that it intersects $AD$ at $P$ and $BC$ at $Q$. Prove that $P, Q, C,$ and $D$ are concyclic.

In a circle with radius $13 \, cm$,find the length of a chord lying at a distance of $12 \, cm$ from the centre. (in $, cm$)