ceva's theorem is a theorem about triangles in plane geometry. given a triangle "abc", let the lines "ao", "bo" and "co" be drawn from the vertices to a common point "o" (not on one of the sides of "abc"), to meet opposite sides at "d", "e" and "f" respectively. (the segments "ad, be," and "cf" are known as cevians.) then, using signed lengths of segments,