# 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.

**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.