|
|
| (45 intermediate revisions by 20 users not shown) |
| Line 1: |
Line 1: |
| − | '''Ceva's Theorem''' is an algebraic statement regarding the lengths of [[cevians]] in a [[triangle]].
| + | #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>
| |
| − | <br>
| |
| − | 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]]
| |
