By : Nayana


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 ?

Pictorial Representation

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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

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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.

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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


The distance is 64 miles .


So in conclusion points of concurrency are used in present day scenarios. The reason that circumcenter is the best point of concurrency for this scenario is because that the situation was building something in the middle of three towns. And the building had to be equidistant from each town so that it was reachable by everyone . Circumcenter is equidistant from the vertices of a triangle . The special segment used to reveal that this scenario needed circumcenter was perpendicular bisector .