Question

A cell phone company is looking to place a new tower to service 3 cities. In order for it to best service each city, it needs to be equidistant from all 3 cities. What mathematical concept could they use to find a location that is equidistant from all 3 cities? Why is this a good method?

Answer 1

• circumscribed circle
• The center of a circle circumscribing the triangle connecting the 3 cities will be equidistant from all three cities.

Explanation:

The circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of the circle, the circumcenter, is equidistant from all of the polygon's vertices.

The center is found at the point of intersection between the perpendicular bisectors of any two (non-parallel) chords of the circle. That is, the perpendicular bisectors of any two of the sides of the triangle joining the cities will intersect at the circumcenter.

The method of locating the center of the circle this way is simple and effective.