The chord which passes through the centre of the circle is called a .......... of the circle.

In a cyclic quadrilateral,$\angle A = 3x + 15^{\circ}$ and $\angle C = 2x + 15^{\circ}$. Find the value of $x$.

$A$ circular park of radius $20\,m$ is situated in a colony. Three boys Ankur,Syed and David are sitting at equal distance on its boundary,each having a toy telephone in his hands to talk with each other. Find the length of the string of each phone.

In the given figure,if $\angle BCD = 40^{\circ}$ and $\angle BAE = 65^{\circ},$ then find the values of $a, b,$ $c$ and $d$.

State whether each of the following statements is true or false:
$(1)$ There are three circles passing through three given non-collinear points.
$(2)$ Infinitely many circles pass through two given points.

$AB$ 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 $, cm$)