Difference between revisions of "Ceva's Theorem"

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== Example ==
 
== Example ==
 
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.
 
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]]

Revision as of 19:46, 18 June 2006

Ceva's Theorem is an algebraic statement regarding the lengths of cevians in a triangle.


Statement

(awaiting image)
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


$BD * CE * AF = +DC * EA * FB$


where all segments in the formula are directed segments.

Example

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.

See also

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