The lengths of two parallel chords of a circle are $6\, cm$ and $8\, cm$. If the smaller chord is at a distance of $4\, cm$ from the centre,what is the distance of the other chord from the centre (in $, cm$)?

Write True or False and justify your answer in each of the following: Two chords $AB$ and $CD$ of a circle are each at distances $4 \ cm$ from the centre. Then $AB = CD$.

In a circle with centre $O$,the lengths of two chords $AB$ and $CD$ are $12 \, cm$ and $16 \, cm$ respectively. If the chord $AB$ is at a distance $8 \, cm$ from the centre,what is the distance of the chord $CD$ from the centre (in $, cm$)?

Three girls Reshma,Salma,and Mandip are playing a game by standing on a circle of radius $5 \, m$ drawn in a park. Reshma throws a ball to Salma,Salma to Mandip,and Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is $6 \, m$ each,what is the distance between Reshma and Mandip (in $, m$)?

If two equal chords of a circle intersect,prove that the parts of one chord are separately equal to the parts of the other chord.

$AB$ and $CD$ are two chords of a circle with centre $P$. The distance of chord $AB$ from the centre $P$ is $15 \, cm$ and the distance of chord $CD$ from the centre $P$ is $8 \, cm$. If $AB = 16 \, cm$,then find the length of chord $CD$. (in $, cm$)