5-35-3Points of ConcurrencyPoints of Concurrency

Objective:Objective:

To identify properties of To identify properties of perpendicular bisectors and angle perpendicular bisectors and angle

bisectorsbisectors

Concurrent: When three or more lines, segments, rays or planes have a point in common.Point of Concurrency: The point of intersection.

Not Concurrent

Concurrent

Point of Concurrency

The three perpendicular bisectors of a triangle are concurrent.Point of concurrency is called circumcenter.

The circumcenter of a triangle is equidistant from the verticesand is the center of the circle.

The circumcenter of a triangle can be inside, on , or outside a triangle.

Finding the Circumcenter of a triangle.

The point of concurrency of the angle bisectors of atriangle is called the incenter of the triangle.

The bisectors of the anglesof a triangle are concurrentat a point equidistant fromthe sides of the triangle.

P is the center of the circlethat is inscribed in the triangle.

p. 305: 7, 8, 9, 15, 17, 37, 38