Cleaver (geometry)

The cleavers and Spieker center of a triangle

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.

• Each cleaver is parallel to one of the angle bisectors of the triangle.
• The three cleavers concur at the center of the Spieker circle.

See also

• Splitter (geometry)

Notes and references

• Ross Honsberger, "Cleavers and Splitters." Chapter 1 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Mathematical Association of America, pages 1–14, 1995.