In a huge park, people are concentrated at three points (see Fig. 7.52):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 maximum number of persons can approach it?(Hint : The parlour should be equidistant from A, B and C).

Explanation

The maximum number of persons can approach the ice-cream parlor if it is equidistant from A, B, and C. In a triangle, the circumcentre is the only point that is equidistant from its vertices.


So, the ice-cream parlor should be set up at the circumcentre O of `ΔAB`C as shown below.





We can find circumcentre O of this triangle by drawing perpendicular bisectors of the sides of this triangle.


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