Orthologic Triangles

Two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 are orthologic if the perpendiculars from the vertices A_1, B_1, C_1 on the sides B_2C_2, A_2C_2, and A_2B_2 are concurrent. Furthermore, if this is the case, then the perpendiculars from the vertices A_2, B_2, C_2 on the sides B_1C_1, A_1C_1, and A_1B_1 are also concurrent, as shown by Steiner in 1827.

The point of concurrence is known as the orthology center of DeltaA_1B_1C_1 with respect to DeltaA_2B_2C_2.

See also

Orthology Center

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Gallatly, W. "Orthologic Triangles." §82 in The Modern Geometry of the Triangle, 2nd ed. London: Hodgson, pp. 55-56, 1913.

Referenced on Wolfram|Alpha

Orthologic Triangles

Cite this as:

Weisstein, Eric W. "Orthologic Triangles." From MathWorld--A Wolfram Web Resource.

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