# The Relationship between the Nine-Point Circle, the Circumscribed Circle and the Inscribed Circle of Archimedes’ Triangle

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Yuporn Rimcholakarn

## Abstract

The purpose of this research was to study the relationship between the Nine-Point Circle and the Circumscribed circle of Archimedes’ triangle, and the relationship between the Nine-Point circle and the Inscribed circle of Archimedes’ triangle. The results were that the radius of the Nine-Point Circle of Archimedes’ triangle is half the radius of the Circumscribed circle of Archimedes’ triangle, and the Nine-Point circle and the Inscribed circle of Archimedes’ triangle touch internally.

Keywords: Archimedes’ triangle, Nine-Point circle, Circumscribed circle of triangle, Inscribed circle of triangle

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