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| − | '''Ceva's Theorem''' is an algebraic statement regarding the lengths of [[cevians]] in a [[triangle]].
| + | #REDIRECT[[Ceva's theorem]] |
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| − | == Statement ==
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| − | ''(awaiting image)''<br>
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| − | A necessary and sufficient condition for AD, BE, CF, where D, E, and F are points of the respective side lines BC, CA, AB of a triangle ABC, to be concurrent is that
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| − | <br><center><math>BD * CE * AF = +DC * EA * FB</math></center><br>
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| − | where all segments in the formula are directed segments.
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| − | == Example ==
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| − | Suppose AB, AC, and BC have lengths 13, 14, and 15. If AF:FB = 2:5 and CE:EA = 5:8. If BD = x and DC = y, then 10x = 40y, and x + y = 15. From this, we find x = 12 and y = 3.
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| − | == See also ==
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| − | * [[Menelaus' Theorem]]
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| − | * [[Stewart's Theorem]]
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