Concurrent lines

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In geometry, three or more lines are said to be concurrent if they intersect at a single point.

In a triangle, four basic types of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors:

• In a triangle, altitudes run from each vertex and meet the opposite side at right-angles. The point where three altitudes meet is the orthocenter.

• Angle bisectors are rays running from the bisector of each angle of the triangle. They all meet at the incenter.

• Medians connect the vertices in a triangle to the midpoint of the opposite side. They meet at the centroid.

• Perpendicular bisectors are lines running out of the midpoint of each side in a triangle at 90 degree angles. They meet at the circumcenter.

Compare to collinear. In projective geometry, concurrency is the dual of collinearity.