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Exploring Triangle Centers: Points of Concurrency & More

Discover the fascinating world of triangle centers, points of concurrency, and their significance in geometry. Learn about key points like Incenter, Circumcenter, Orthocenter, and Centroid, along with newer points like Fermat Point and Nine-Point Center.

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Exploring Triangle Centers: Points of Concurrency & More

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  1. Triangle Centers • What are they? • Where are they? • How are they found?

  2. Triangle Centers Points of Concurrency • Whatis 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 concurrentlines.

  3. 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.

  4. Incenter • Point of concurrency formed by the intersection of the three bisectors of a triangle Incenter

  5. CIRCUMCENTER • Point of concurrency formed by the intersection of three perpendicular bisectors of the sides of a triangle Circumcenter

  6. ORTHOCENTER • Point of concurrency formed by the intersection of the three altitudes of a triangle Orthocenter

  7. Centroid • Point of concurrency formed by the intersection of the three medians of a triangle Centroid

  8. 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…..

  9. The Points are… angle bisectors • Incenter • Circumcenter • Orthocenter • Centroid perpendicular bisectors altitudes medians

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