Question

Question 3
In a huge park people are concentrated at three points (see the given figure)

A: where there are different slides and swings for children,
B: near which a man-made lake is situated,
C: which is nearto a large parking and exit.
Where should an ice-cream parlour be set up so that maximum number of persons can approach it?

Answer 1

Maximum number of persons can approach the ice-cream parlour if it is equidistant from A, B and C. Now, A, B and C form a triangle. In a triangle, the circumcentre is the only point that is equidistant from its vertices. So, the ice-cream parlour should be set up at the circumcentre O of $\Delta$ABC.

In this situation, maximum number of persons can approach it. We can find circumcentre O of this triangle by drawing perpendicular bisectors of the sides of this triangle.