In a huge park,people are concentrated at three points (see Fig) :
$A$ : where there are different slides and swings for children,
$B$ : near which a man-made lake is situated,
$C$ : which is near to a large parking and exit. Where should an ice cream parlour be set up so that the maximum number of persons can approach it?
(Hint: The parlour should be equidistant from $A$,$B$,and $C$.)

(N/A) To ensure the ice cream parlour is equidistant from points $A$,$B$,and $C$,we need to find the circumcenter of the triangle formed by these points.
$1$. Join points $A$ and $B$,and draw line $l$,which is the perpendicular bisector of segment $AB$.
$2$. Join points $B$ and $C$,and draw line $m$,which is the perpendicular bisector of segment $BC$.
$3$. Let the perpendicular bisectors $l$ and $m$ intersect at point $O$.
Point $O$ is the circumcenter of $\triangle ABC$,and it is equidistant from vertices $A$,$B$,and $C$. Therefore,the ice cream parlour should be set up at point $O$.