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.

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

Circumcenter is the point where the company place the tower because it is a point of intersection of all the perpendicular bisectors of the sides and it is also the center of the circumcircle.

Given :

Given that the cell phone company wants to place a new cell tower so that it is the same distance from the centers of the three towns, it means that a point inside a triangle from where all the vertices of a triangle are at same distance.

Therefore, circumcenter is the point where the company place the tower because it is a point of intersection of all the perpendicular bisectors of the sides and it is also the center of the circumcircle.

For more information, refer the link given below:

link

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