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Crucial Point

The Homothetic Center of the Orthic Triangle and the triangular hull of the three Excircles. It has Triangle Center Function

\alpha=\tan A=\sin(2B)+\sin(2C)-\sin(2A).


Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Lyness, R. and Veldkamp, G. R. Problem 682 and Solution. Crux Math. 9, 23-24, 1983.

© 1996-9 Eric W. Weisstein