The broken chord theorem of Archimedes provides another construction of the cleaver. Suppose the triangle to be bisected is ABC, and that one endpoint of the cleaver is the midpoint of side AB. Form the circumcircle of ABC and let M be the midpoint of the arc of the circumcircle from A to B through C. Then the other endpoint of the cleaver is the closest point of the triangle to M, and can be found by dropping a perpendicular from M to the longer of the two sides AC and BC.
- Honsberger, Ross (1995), "Chapter 1: Cleavers and Splitters", Episodes in Nineteenth and Twentieth Century Euclidean Geometry, New Mathematical Library, 37, Washington, DC: Mathematical Association of America, pp. 1–14, ISBN 0-88385-639-5, MR 1316889
- Avishalom, Dov (1963), "The perimetric bisection of triangles", Mathematics Magazine, 36 (1): 60–62, JSTOR 2688140, MR 1571272