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 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 parlor should be equidistant from A, B and C)
Answer:
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 ∆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.
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