Basic Parameters of the Orthocenter

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The orthocenter of a triangle [1] is the intersection of its three altitudes.


Let , , be the side lengths opposite the corresponding vertices and , , be the circumradius, inradius and semiperimeter of .

Let , , be the exact trilinear coordinates of and be the sum of the exact trilinear coordinates of the point .



, , are the Conway parameters with ,

is the cevian triangle and pedal triangle of .





You can drag the vertices , and .


Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA



A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.

Standard barycentric coordinates of a point with respect to a reference triangle are normalized to have a sum of 1.


[1] Encyclopedia of Triangle Centers (ETC).

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