# Concurrent Lines, Medians, and Altitude: Geometry Help

Help with concurrent lines, point of concurrency, perpindicular bisectors, angle bisectors, circumcenters of triangles, and incenters of triangles.

#### Definition: Concurrent Lines

__ Concurrent Lines__ are three or more lines intersecting at one point.

#### Definition: Point of Concurrency

The ** Point of Concurrency** is the point where concurrent lines intersect.

### Theorem

Perpendicular bisectors of sides of a triangle are concurrent at a point equidistant from the vertices.

#### Definition: Circumcenter of Triangle

The __ Circumcenter of a Triangle__is the point of concurrency of the perpendiculars of a triangle.

For example, in the picture below, the three perpendicular bisectors(M¹, M², M³) intersect at point O. That makes point O the circumcenter of the triangle. It is also the center of the circle surrounding the triangle. Therefore, the circle is “circumscribed” about the triangle.

### Theorem

Angle bisectors of a triangle are concurrent at a point equidistant from the sides.

#### Definition: Incenter of Triangle

The ** Incenter of a Triangle** is the point of concurrency of the angle bisectors.

For example, in the picture below, the three angle bisectors(t¹, t², t³) intersect at point I, making point I the incenter and also the center of the circle. Therefore, the circle is inscribed in the triangle.

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On October 5, 2010 at 1:17 pm

thanks it helped out a lot