Math CentralQuandaries & Queries


Question from BandNerd, a student:

I need to find the circumcenter of the triangle with the coordinates A(0,0) B(12,6) and C(18,0). I do not understand how to solve it algebraically. Please help!

While there is a formula for the circumcenter of any triangle (which you can find on the internet), the vertices have been chosen in your problem so that it is easier just to find the point where the perpendicular bisectors of the sides meet. I assume you know how to find perpendicular bisectors:

One is the vertical line halfway between A and C.
Another easy one is the perpendicular to the line AB that passes halfway between (0,0) and (12,6).

You just need those two lines. The point you seek is where those two perpendicular bisectors meet. I recommend drawing a diagram to check your answer.


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS