Difference between revisions of "Ceva's Theorem"

(Statement)
(Statement)
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== Statement ==
 
== Statement ==
***awaiting image***
+
''(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
 
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
 
<br><center><math>BD * CE * AF = +DC * EA * FB</math></center><br>
 
<br><center><math>BD * CE * AF = +DC * EA * FB</math></center><br>

Revision as of 20:35, 18 June 2006

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.

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