Splitter (geometry)

  Arbitrary triangle △ABC
  Excircles, tangent to the sides of △ABC at TA, TB, TC
  Extouch triangle △TATBTC
  Splitters of the perimeter ATA, BTB, CTC; intersect at the Nagel point N

In Euclidean geometry, a splitter is a line segment through one of the vertices of a triangle (that is, a cevian) that bisects the perimeter of the triangle.[1][2] They are not to be confused with cleavers, which also bisect the perimeter but instead emanate from the midpoint of one of the triangle's sides.

  1. ^ Honsberger, Ross (1995), "Chapter 1: Cleavers and Splitters", Episodes in Nineteenth and Twentieth Century Euclidean Geometry, New Mathematical Library, vol. 37, Washington, DC: Mathematical Association of America, pp. 1–14, ISBN 0-88385-639-5, MR 1316889
  2. ^ Avishalom, Dov (1963), "The perimetric bisection of triangles", Mathematics Magazine, 36 (1): 60–62, JSTOR 2688140, MR 1571272