The Theorem of Ceva

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 />
 $

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