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)

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Question

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 circum centre is the only point that is equidistant from its vertices.

So, the ice-cream parlour should be set up at the circum centre O of ∆ABC

In this situation,

Maximum number of persons can approach it.

We can find circum centre O of this triangle by drawing perpendicular bisectors of the sides of this triangle

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