Ceva's Theorem
Ceva's Theorem is an algebraic statement regarding the lengths of cevians in a triangle.
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 
and 
. Find BD and DC.
If 
and 
, then 
, and 
. From this, we find 
and 
.
