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Math Help - Help with proof involving Cevians.

  1. #1
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    Help with proof involving Cevians.

    Given \Delta ABC as shown with AF=\frac{1}{4} AB , AE=\frac{1}{4} AC and \overline{BE} \cap \overline{CF}=0 prove AO hits \overline{BC} at its midpoint.

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  2. #2
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    Quote Originally Posted by jpatrie View Post
    Given \Delta ABC as shown with AF=\frac{1}{4} AB , AE=\frac{1}{4} AC and \overline{BE} \cap \overline{CF}=0 prove AO hits \overline{BC} at its midpoint.

    Let {D}= AO intersection BC

    Use Ceva Theorem:

    \frac{AF}{FB} * \frac{BD}{DC} * \frac{CE}{EA}=1

    Simplify and obtain the ratio BD : DC
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