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# Ceva's theorem (lines from vertices to the opposite sides of a triangle)

## Description

Ceva’s theorem is a theorem about triangles in Euclidean plane geometry. Given a triangle ABC, let the lines AO, BO and CO be drawn from the vertices to a common point O to meet opposite sides at D, E and F respectively. Then, using signed lengths of segments, there is a relation between the segments. In other words the length AB is taken to be positive or negative according to whether A is to the left or right of B in some fixed orientation of the line. For example, AF/FB is defined as having positive value when F is between A and B and negative otherwise.

Related formulas

## Variables

 AF Segment on AB side of the triangle (dimensionless) FB Other Segment on AB side of the triangle (dimensionless) BD Segment on BC side of the triangle (dimensionless) DC Other Segment on BC side of the triangle (dimensionless) CE Segment on AC side of the triangle (dimensionless) EA Other Segment on AC side of the triangle (dimensionless)