Splitter (geometry)
Encyclopedia
In plane geometry
, a splitter of a triangle
is a line segment having one endpoint at one of the three vertices of the triangle and the other so located on the perimeter as to bisect the perimeter.
The three splitters concur
at the Nagel point
of the triangle.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a splitter of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is a line segment having one endpoint at one of the three vertices of the triangle and the other so located on the perimeter as to bisect the perimeter.
The three splitters concur
Concurrent lines
In geometry, two or more lines are said to be concurrent if they intersect at a single point.In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors:...
at the Nagel point
Nagel point
In geometry, the Nagel point is a point associated with any triangle. Given a triangle ABC, let TA, TB, and TC be the extouch points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively...
of the triangle.