Cosymmedian Triangles

Extend the symmedians of a triangle DeltaA_1A_2A_3 to meet the circumcircle at P_1, P_2, P_3. Then the symmedian point K of DeltaA_1A_2A_3 is also the symmedian point of DeltaP_1P_2P_3. The triangles DeltaA_1A_2A_3 and DeltaP_1P_2P_3 are cosymmedian triangles, and have the same Brocard circle, second Brocard triangle, Brocard angle, Brocard points, and circumcircle.

See also

Brocard Angle, Brocard Circle, Brocard Points, Brocard Triangles, Circumcircle, Comedian Triangles, Symmedian, Symmedian Point

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Lachlan, R. An Elementary Treatise on Modern Pure Geometry. London: Macmillian, p. 63, 1893.

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Cosymmedian Triangles

Cite this as:

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

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