$AB$ and $CD$ are two parallel chords of a circle with centre $P$. Also,the centre $P$ lies between $AB$ and $CD$. If $AB = 48 \, cm$,$CD = 40 \, cm$,and the radius of the circle is $25 \, cm$,find the distance between $AB$ and $CD$. (in $, cm$)

In a circle with centre $P$,$AB$ and $CD$ are equal chords. If $\angle APB = 100^{\circ}$,then find $\angle PCD$. (in $^{\circ}$)

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 $, m$)?

In a circle with centre $O$,two chords $PQ$ and $RS$ subtend equal angles at the centre. If $PQ = 12 \text{ cm}$,then $RS = \dots \text{ cm}$.

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 $AB = CD$.

If two equal chords of a circle intersect within the circle,prove that the line joining the point of intersection to the centre makes equal angles with the chords.