\input zb-basic \input zb-matheduc \iteman{ZMATH 2016c.00754} \itemau{Contreras, Jos\'e N.} \itemti{Discovering, applying, and extending Ceva's theorem.} \itemso{Math. Teach. (Reston) 108, No. 8, 632-637 (2015).} \itemab From the text: Among the most commonly known points of concurrency are the four points of intersection classically associated with a triangle: the centroid, the orthocenter, the incenter, and the circumcenter. Armed with two extremely powerful theorems from elementary geometry -- Ceva's theorem and its converse, here referred to simply as Ceva's theorem -- I take my college geometry class on a journey to simplify and unify the proofs of classical concurrency theorems. \itemrv{~} \itemcc{G45 G75 U75} \itemut{geometry; Ceva's theorem; triangles; cevians; division points; ratios; concurrence; proofs; similarity; centroid; medians; orthocenter; altitudes; incenter; angle bisectors; circumcenter; perpendicular bisectors; interior angle bisector theorem; medial triangle; points of concurrency; Gergonne point; Nagel point; Lemoine point; Fermat point; generalization; polygons with an odd number of sides} \itemli{http://www.nctm.org/Publications/mathematics-teacher/2015/Vol108/Issue8/Discovering,-Applying,-and-Extending-Ceva\_s-Theorem/} \end