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# 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 icecream parlour be set up so that maximum number of persons can approach it?

(Hint: The parlour should be equidistant from A, B and C)

**Solution:**

The maximum number of persons can approach the ice-cream parlour if it is equidistant from A, B and C. 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 as shown below.

We can find circumcentre O of this triangle by drawing perpendicular bisectors of the sides of this triangle.

In this situation, the maximum number of people can approach it.

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 7

**Video Solution:**

## 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 icecream parlour be set up so that maximum number of persons can approach it?

(Hint: The parlour should be equidistant from A, B and C)

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.5 Question 3

**Summary:**

We should set up the ice-cream parlour at the circumcentre(O) of ΔABC as the parlour will be equidistant from A, B and C so that the maximum number of persons can approach it.

**☛ Related Questions:**

- Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
- ABC is a triangle. Locate a point in the interior of ∆ABC which is equidistant from all the vertices of ∆ABC.
- In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
- Complete the hexagonal and star shaped Rangolies (see Fig. 7.53 (i) and (ii)) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

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