Wyatt and his friends Diamond, Darnell, and Amy are playing a war combat game online. His friends' characters have holed up in three defensive positions at some distance from their base camp. Wyatt's character is the team healer, and he may need to race to any of the three locations at a moment's notice to help one of his teammates.
He is poring over a map showing his friends' locations. How can he locate the spot in the middle that is exactly the same distance from each of his friends?
The locations of the friends will form vertexes of a triangle
If we construct perpendicular bisectors of each side of this triangle.....they willl neet at the circumcenter.....
This will be the center of a circle that will pass through each vertex....so.....the radial distance from this point to each of his friends will be equal
[BTW...this point could lie outside the triangle !!! ]
Here's a good resource to show this : http://www.mathopenref.com/trianglecircumcenter.html