Difference between revisions of "Ceva's Theorem"

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'''Ceva's Theorem''' is an algebraic statement regarding the lengths of [[Cevian|cevians]] in a [[triangle]].
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#REDIRECT[[Ceva's theorem]]
 
 
 
 
== Statement ==
 
''(awaiting image)''<br>
 
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>
 
where all segments in the formula are directed segments.
 
 
 
== Example ==
 
Suppose AB, AC, and BC have lengths 13, 14, and 15.  If <math>\frac{AF}{FB} = \frac{2}{5}</math> and <math>\frac{CE}{EA} = \frac{5}{8}</math>.  Find BD and DC.<br>
 
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If <math>BD = x</math> and <math>DC = y</math>, then <math>10x = 40y</math>, and <math>{x + y = 15}</math>.  From this, we find <math>x = 12</math> and <math>y = 3</math>.
 
 
 
== See also ==
 
* [[Menelaus' Theorem]]
 
* [[Stewart's Theorem]]
 

Latest revision as of 15:06, 9 May 2021

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