# 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) |