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? Explain.

Answer 1

Answer:

Sample Response: 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.

Answer 2

we know that

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. It is also the center of the circumcircle, the circle that passes through all three vertices of the triangle

The distance of the circumcenter to the vertices of the triangle is equal to the radius of the circle

see the attached figure to better understand the problem

therefore

the answer is

The cell phone company must be place the new cell tower in the circumcenter of the triangle formed by the center of the three towns