Splitter (geometry)

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.

[3] The three splitters concur at the Nagel point of the triangle,[1] which is also called its splitting center.

[2] Some authors have used the term "splitter" in a more general sense, for any line segment that bisects the perimeter of the triangle.

Other line segments of this type include the cleavers, which are perimeter-bisecting segments that pass through the midpoint of a triangle side, and the equalizers, segments that bisect both the area and perimeter of a triangle.

Arbitrary triangle △ ABC
Excircles , tangent to the sides of △ ABC at T A , T B , T C
Extouch triangle △ T A T B T C
Splitters of the perimeter AT A , BT B , CT C ; intersect at the Nagel point N