The Theorem of Ceva

Submitted by Isoscel on Fri, 08/24/2007 - 20:00.

In a triangle ABC, if we have $A_1$ on $BC$ , $B_1$ on $CA$ and $C_1$ on $AB$ then $AA_1$ , $BB_1$ and $CC_1$ are concurrent if and only if:

$<br /> \frac{AC_1}{C_1B}\,\cdot\,\frac{BA_1}{A_1C}\,\cdot\,\frac{CB_1}{B_1A}=1<br />$