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Geometry

Triangle Centers

Intro

It might seem like one definition of “center” should be enough for any shape, but even for the ‘simple’ triangle, there are actually four important types of centers: the centroid, the circumcenter, the incenter, and the orthocenter.

Expect to see and learn how to solve questions like this one:

As exemplified in the question above, each type of center can be studied and applied independently. However, the most intriguing mathematical conclusions we can draw follow from comparing the positions of all four centers. While the four centers are seldom in the same location, it can be very useful to know that three of these center types are always on a single line known as the Euler line.

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