Difference between revisions of "Ceva's Theorem"
(→Statement) |
(→Statement) |
||
| Line 1: | Line 1: | ||
== Statement == | == Statement == | ||
| − | ''(awaiting image)'' | + | ''(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 | 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 19:35, 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
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.
