# Ex.7.5 Q3 Triangles Solution - NCERT Maths Class 9

## Question

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

## Text Solution

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 \(C\))

**Steps:**

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 \(\Delta ABC\).

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.