what are they? where are they? how are they found?

• What are they?• Where are they?• How are they found?

Triangle Centers Points of Concurrency

• What is this all about?A Point of Concurrency is a point

of intersection of 2 or more lines. The lines that form a point

concurrency are called concurrent lines.

The Points are…The Points are…

• Incenter• Circumcenter• Orthocenter• Centroid

• Though there are many other points of concurrency, which we will see later, we will concentrate on these four today.

Incenter• Point of concurrency formed by the

intersection of the three bisectors of a triangle

CIRCUMCENTERCIRCUMCENTER• Point of concurrency formed by the

intersection of three perpendicular bisectors of the sides of a triangle

ORTHOCENTER• Point of concurrency formed by the

intersection of the three altitudes of a triangle

Centroid• Point of concurrency formed by the

intersection of the three medians of a triangle

Oh yeah, in case you are wondering, here are some other more recent pts. of concurrency.

• Fermat Point• Nine-Point Center• Symmedian Point• Nagel Point• Napolean Point• Schiffler Point• Exeter Point• Apollonious Point• Parry Point• And the list could go on and on and on…..

The Points are…The Points are…

• Incenter• Circumcenter • Orthocenter • Centroid