Question

The city council is planning to construct a park on North Street that has a triangular perimeter. They want to place a fountain at a point equidistant from all three sides of the park. Where should the council place the fountain?

Answer 1

In-center of the triangular park.

Explanation:

Since city council is planning to construct a park on North street that has a triangular perimeter.

We know "Incenter" of a triangle is a point inside the triangle, equidistant from all sides of the triangle.

Moreover, "Incenter" is the point of intersection of all angle bisectors of the triangle.

So city council should place the fountain at "Incenter" of the triangular park.

Answer 2

In this case they would want to put the fountain exactly in the middle of the triangle, since "equidistant" in this case means "equally distant", and this occurs at the exact center of the triangle.