Difference between revisions of "Ceva's Theorem"
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== Example == | == 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. | 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. | ||
| + | |||
| + | == See also == | ||
| + | * [[Menelaus' Theorem]] | ||
| + | * [[Stewart's Theorem]] | ||
Revision as of 19:46, 18 June 2006
Ceva's Theorem is an algebraic statement regarding the lengths of cevians in a triangle.
Statement
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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.
