Finding the Center of the Research Triangle

Date: 9/5/95 at 10:24:17
From: Anonymous
Subject: Center of a triangle

Hi.  We live in an area known as the Research Triangle, with the triangle's 
points at the University of North Carolina, North Carolina State University 
and Duke University.  We are interested in finding the center point of our 
triangle home and whether there is a unique term (or several terms) for the 
center point of a triangle (is it just centroid?).  Is the center point the 
intersection of the three lines connecting the triangle's points with the 
midpoints of the opposite lines?  

Thanks for your help.

Date: 9/8/95 at 16:58:52
From: Doctor Ken
Subject: Re: Center of a triangle

Hello!

There is actually more than one option you have for the center of a triangle.
One center is the center of the inscribed circle: you can find it by finding
the point at which the angle bisectors meet inside the triangle.  Another
is the center of the circumscribed circle: you can find it by finding the 
point at which the perpendicular bisectors of each side meet.  A third is
the "center of mass": it is the intersection of the three lines connecting
the triangle's vertices with the midpoints of the opposite lines, the one
about which you spoke.  

Perhaps you should choose which one you want based on which one is 
in the best location in the U.S.!

- Doctor Ken,  The Geometry Forum