In the plane of any triangle ABC, let

D = the point where (altitude through A) meets side BC,
E = the point where (altitude through B) meets side CA,
F = the point where (altitude through C) meets side AB.

As you see in the sketch, the three altitudes all come together in one point, called the orthocenter of triangle ABC. Along with the centroid, incenter, and circumcenter, the orthocenter and some of its properties were known to the ancient Greeks.

Triangle Centers
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