altitude triangle

Given a triangle Δ A B C, the triangle Δ H_A H_B H_C whose vertices are endpoints of the altitudes from each of the vertices of Δ A B C is called the orthic triangle, or sometimes the altitude triangle. The three lines A H_A, B H_B, and C H_C are concurrent at the orthocenter H of Δ A B C. The orthic triangle is therefore both the pedal triangle and Cevian triangle with respect to H. It is also the cyclocevian triangle of the triangle centroid G. Its trilinear vertex matrix is [0 | sec B | sec C sec A | 0 | sec C sec A | sec B | 0].

altitude | Fagnano's problem | orthic inconic | orthocenter | pedal triangle | symmedian point