# Menelaus’ theorem

If the points $X$, $Y$ and $Z$ are on the sides of a triangle $ABC$ (including their prolongations), collinear and do not coincide with any of the points $A$, $B$ and $C$, then the equation

 $\frac{AZ}{ZB}\cdot\frac{BY}{YC}\cdot\frac{CX}{XA}=-1$

holds (all segments are directed line segments). The converse of this theorem also holds (thus: three points on the prolongations of the triangle’s sides are collinear if the above equation holds).

Title Menelaus’ theorem MenelausTheorem 2013-03-22 12:46:20 2013-03-22 12:46:20 mathwizard (128) mathwizard (128) 7 mathwizard (128) Theorem msc 51A05 CevasTheorem TrigonometricVersionOfCevasTheorem Collinear