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Let ABC be a triangle, and let D, E, F be points on lines BC, CA, AB, respectively. Lines AD, BE, CF are concurrent if and only if

$\frac{BD}{DC} \cdot \frac{CE}{EA}\cdot \frac{AF}{FB} = 1,$

where lengths are directed. This also works for the reciprocal or each of the ratios, as the reciprocal of 1 is 1.

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current09:26, 18 August 2006Thumbnail for version as of 09:26, 18 August 2006344 × 186 (6 KB)Joml88 (talk | contribs)
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