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
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