The characterizations of triangles using the nine-point circles

Abstract

In this note, primarily intended for high school students and high school teachers, characterizations of a right triangle and an equilateral triangle in the Euclidean plane are presented using the nine-point circle of a given triangle. Geometrical applications are explored along with their possible uses in the teaching environment.

Keywords:

• Pythagorean theorem
• circumcircle
• nine-point circle
• the orthocentre

AMS Subject Classification:

• 11R04