The lines AK_A, BK_B, and CK_C which are isogonal to the triangle medians AM_A, BM_B, and CM_C of a triangle are called the triangle's symmedian. The symmedians are concurrent in a point K called the symmedian point which is the isogonal conjugate of the triangle centroid G.

The triangle DeltaK_AK_BK_C formed by the intersections of the symmedians with the sides of the reference triangle is known as the symmedial triangle.

See also

Isogonal Conjugate, Symmedian Point, Symmedial Triangle, Triangle Centroid, Triangle Median

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Casey, J. "Theory of Isogonal and Isotomic Points, and of Antiparallel and Symmedian Lines." Supp. Ch. §1 in A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 165-173, 1888.Coolidge, J. L. A Treatise on the Geometry of the Circle and Sphere. New York: Chelsea, p. 65, 1971.Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 213-218, 1929.Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, pp. 62-63, 1893.Mackay, J. S. "Symmedians of a Triangle and Their Concomitant Circles." Proc. Edinburgh Math. Soc. 14, 37-103, 1896.

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Cite this as:

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

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