# In a huge park people are concentrated at three points (see the given figure): - Mathematics

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)

#### Solution

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 ΔABC. 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.

Concept: Inequalities in a Triangle
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Chapter 7: Triangles - Exercise 7.5 [Page 133]

#### APPEARS IN

NCERT Class 9 Maths
Chapter 7 Triangles
Exercise 7.5 | Q 3 | Page 133

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