In a huge park, people are concentrated at three points (see figure):

A: where there are different slides and swings for children.

B: near which a man-made lake is situated.
C: which is near a large parking and exit.
Where an ice cream parlor is set up so that the maximum number of persons can approach it?

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At A

At B

At C

None of these

answer is D.

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Detailed Solution

The given park is,
Question Image

Join the given points A, B, C and form a triangle

Δ A B C .

Maximum number of persons can approach the ice-cream parlor if it is equidistant from the points A, B, and C.
Since the points A, B and C form a triangle and we know that 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 ΔABC.
Hence, option (4) is correct.

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