# Circumcenter

## Problem

A county plans to build a fire station to save the people from the wild fires that occur. The county has 3 towns that the wild fires occur at. The towns are sparkville , reighnsville and mystic Ville. The county wants the fire station equidistant from all 3 towns . Which point of concurrency should they use to find where to place the fire station ?

## Construction

The point of concurrency you use is circumcenter. The circumcenter of a triangle is equidistant from the vertices of the triangle . But how do you find the circumcenter of the triangle made by the towns ? . The link below shows you how to draw a circumcenter

## Problem 2

There is a fire in reighnsville and the firefighters need to get there fast . How far reighnsville from the fire station.

use the information in the picture below to solve the problem.

## How to solve the problem

according to the picture it is given that segment FS is 64 miles . It is also given that segments AF , BF and CF are perpendicular bisectors .

Since all that information is given you can conclude that :

FS = FR = FM by the circumcenter theorem

Now you can find the distance of segment FR ( fire station to Reignsville)

FS = FR Given

FS = 64 Given

FR = 64 by substitution