Triangle Centers

Chapter 7 of AoPS Introduction to Geometry covers all the “centers” of a triangle:  incenter, orthocenter, circumcenter, and centroid.  This is a tricky chapter and it’s easy to get confused with new each section and each new center.  It helps to review what you’ve learned so far before moving on to a new center.  You should be able to do a quick back-of-the-envelope derivation of each center:  for example, because all points on an angle bisector are equidistant from 2 sides, the intersection of the angle bisectors is equally distant from all 3 sides of the triangle and is therefore the center of the inscribed circle, aka, the incenter.

incenter_750

(Source: Wikipedia)

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