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The Lemoine Point of the Excentral Triangle, i.e., the point of concurrence $M$ of the lines from the Excenters $J_i$ through the corresponding Triangle side Midpoint $M_i$. It is also called the Middlespoint and has Triangle Center Function

\alpha=b+c-a={\textstyle{1\over 2}}\cot A.

See also Excenter, Excentral Triangle, Nagel Point


Baptist, P. Die Entwicklung der Neueren Dreiecksgeometrie. Mannheim: Wissenschaftsverlag, p. 72, 1992.

Eddy, R. H. ``A Generalization of Nagel's Middlespoint.'' Elem. Math. 45, 14-18, 1990.

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

Kimberling, C. ``Mittenpunkt.''

© 1996-9 Eric W. Weisstein