Difference between revisions of "Concurrence"

Revision as of 17:49, 23 November 2007

This is an AoPSWiki Word of the Week for Nov 22-28

Several lines (or curves) are said to concur at a point if they all contain that point.

In analytical geometry, one can find the points of concurrency of any two lines by solving the system of equations of the lines.

Ceva's Theorem gives a criteria for three cevians of a triangle to be concurrent. In particular, the three altitudes, angle bisectors, medians, symmedians, and perpendicular bisectors (which are not cevians) of any triangle are concurrent, at the orthocenter, incenter, centroid, Lemoine point, and circumcenter, respectively.

This article is a stub. Help us out by expanding it.

@@ Line 6: / Line 6: @@
 In analytical geometry, one can find the points of concurrency of any two lines by solving the system of equations of the lines.
-[[Ceva's Theorem]] gives a criteria for three [[cevian]]s of a triangle to be concurrent. In particular, the three [[altitude]]s, [[angle bisector]]s, [[median]]s, [[symmedian]]s, and perpendicular bisectors (which is not a cevian) of any triangle are concurrent, at the [[orthocenter]], [[incenter]], [[centroid]], [[circumcenter]], and [[Lemoine point]] respectively.
+[[Ceva's Theorem]] gives a criteria for three [[cevian]]s of a triangle to be concurrent. In particular, the three [[altitude]]s, [[angle bisector]]s, [[median]]s, [[symmedian]]s, and [[perpendicular bisector]]s (which are not cevians) of any triangle are concurrent, at the [[orthocenter]], [[incenter]], [[centroid]], [[Lemoine point]], and  [[circumcenter]], respectively.
 {{stub}}