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Given a triangle $ABC$, and points $D$, $E$, and $F$ on the sides $BC$, $CA$, and $AB$ respectively, then the segments $AD$, $BE$ and $CF$ are concurrent if and only if

$$\dfrac{AF}{FB}\dfrac{BD}{DC}\dfrac{CE}{EA}=1$$

Suppose that the three segments are concurrent in a point $O$