![]() ![]() Thus if there are three of them, they concur at the incenter. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter, and each triangle has one, two, or three of these lines.The three splitters concur at the Nagel point of the triangle. A splitter of a triangle is a line segment having one endpoint at one of the three vertices of the triangle and bisecting the perimeter.The three cleavers concur at the center of the Spieker circle, which is the incircle of the medial triangle. A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides.Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. ![]() Other sets of lines associated with a triangle are concurrent as well. The three perpendicular bisectors meet at the circumcenter. Perpendicular bisectors are lines running out of the midpoints of each side of a triangle at 90 degree angles.Medians connect each vertex of a triangle to the midpoint of the opposite side.Angle bisectors are rays running from each vertex of the triangle and bisecting the associated angle.The point where the three altitudes meet is the orthocenter. A triangle's altitudes run from each vertex and meet the opposite side at a right angle.In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point. ![]()
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