Cleaver (geometry)

**Construction of the Spieker center via cleavers.**
  Triangle $△ ABC$

  Angle bisectors of $△ ABC$ (concurrent at the incenter $I$ )

  **Cleavers** of $△ ABC$ (concurrent at the Spieker center $S$ )

  Medial triangle $△ DEF$ of $△ ABC$

  Inscribed circle of $△ DEF$ (the Spieker circle; centered at $S$ )

In geometry, a cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. They are not to be confused with splitters, which also bisect the perimeter, but with an endpoint on one of the triangle's vertices instead of its sides.