Brocard Inellipse


The Brocard inellipse is the inconic with parameters


giving the trilinear equation


It has the Brocard points Omega and Omega^' of a triangle as its foci and the Brocard midpoint as its center.

Its Brianchon point is the symmedian point K of the triangle, and the triangle formed by the points of contact of the inellipse with the reference triangle is the symmedial triangle, which is also its polar triangle.

It has semiaxes lengths


giving area


where Delta is the area of the reference triangle.

It passes through the points X_(1015), X_(1017), X_(1977), X_(2028), and X_(2029) (Weisstein, Oct. 16 and Nov. 22, 2004).

This inconic is always an ellipse.

See also

Inconic, Inellipse, Symmedial Triangle, Symmedian Point

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Cite this as:

Weisstein, Eric W. "Brocard Inellipse." From MathWorld--A Wolfram Web Resource.

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