Transcript Point of Concurrency

5-3
Points of Concurrency
Objective:
To identify properties of
perpendicular bisectors and angle
bisectors
Concurrent: When three or more lines, segments,
rays or planes have a point in common.
Point of Concurrency: The point of intersection.
Point of
Concurrency
Concurrent
Not Concurrent
The three perpendicular bisectors of a triangle are
concurrent.
Point of concurrency is called circumcenter.
The circumcenter of a triangle is
equidistant from the vertices
and 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 a
triangle is called the incenter of the triangle.
The bisectors of the angles
of a triangle are concurrent
at a point equidistant from
the sides of the triangle.
P is the center of the circle
that is inscribed in the triangle.