Difference between revisions of "Ceva's Theorem"

Latest revision as of 15:06, 9 May 2021

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-== Statement ==
+#REDIRECT[[Ceva's theorem]]
-***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
-<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 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.