Question

Three highways connect the centers of three towns and form a triangle. A cell phone company wants to place a new cell tower so that it is the same distance from the centers of the three towns. How can the company find where to place the tower?

Answer 1

For the tower to be the same distance from each of the centers, the company must find the point that is equidistant from the vertices of the triangle. This is the circumcenter of the triangle and can be found by constructing the point of concurrency of the perpendicular bisectors of the triangle.

Step-by-step explanation:

sample response

Answer 2

This is only possible when the triangle that is formed by the 3 towns is an equilateral triangle, so that the center will have the same distance in each town. Assuming an equilateral triangle, the center is at 1/3 of the height of the equilateral triangle