The Relationship between the Nine-Point Circle, the Circumscribed Circle and the Inscribed Circle of Archimedes’ Triangle
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Published
Sep 24, 2018
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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
References
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Rimcholakarn, Y. (2017). Relationship between area of Archimedes’ Parabolic Segment and area of Archimedes’Triangle. Naresuan University Journal Science and Technology, 25(1), 158-167.
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Yiu, P. (1998). Euclidean Geometry. Florida: Florida Atlantic University.
Yiu, P. (2001). Introduction to the Geometry of the Triangle. Florida: Florida Atlantic University.
Court, N. A. (1980). College Geometry (2nd ed.). New York: Dover Publication, Inc.
Davis, T. (2002). Four Points on a Circle. Retrieved May 29, 2015, from http://www.geometer.org/ mathcircles
Dekov, D. (2009). Computer-Generated Mathematics: the Feuerbach Point. Journal of Computer-Generated Euclidean Geometry, 3, 1-6.
Dunham, W. (1998). Euler the Master of Us all. Washington, DC: the Mathematical Association of America.
Erbas, K. A. (2000). An Explanatory Approach to Archimedes's Quadrature of the Parabola. Retrieved from http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/emat6690/essay1/ essay1.html
Hung, F. (2011). Radius of 9-Points Circle Half of Circumradius. Retrieved from http://www.hkedcity. net/ihouse/fh7878/
Krishna, D. N. V. (2016). Yet Another New Proof of Feuerbach’s theorem. Global Journal of Science Frontier Research (F), 14(1), 9-16.
Manoosilp, P. (2014).the relationship between the Centroid of Archimedes’ Parabolic Segment and the Centroid of Archimedes’ Triangle. Srinakharinwirot Science Journal, 30(2), 151-165.
Rimcholakarn, Y. (2017). Relationship between area of Archimedes’ Parabolic Segment and area of Archimedes’Triangle. Naresuan University Journal Science and Technology, 25(1), 158-167.
Woltermann, M. (2014). Archimedes’ Squaring of Parabola. Retrieved from www2.washjeff.edu/users/ mwoltermann/Dorrie/56.pdf
Yiu, P. (1998). Euclidean Geometry. Florida: Florida Atlantic University.
Yiu, P. (2001). Introduction to the Geometry of the Triangle. Florida: Florida Atlantic University.
Section
Research Articles
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How to Cite
RIMCHOLAKARN, Yuporn.
The Relationship between the Nine-Point Circle, the Circumscribed Circle and the Inscribed Circle of Archimedes’ Triangle.
Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 26, n. 3, p. 63-79, sep. 2018.
ISSN 2539-553X.
Available at: <https://www.journal.nu.ac.th/NUJST/article/view/Vol-26-No-3-2018-63-79>. Date accessed: 26 apr. 2024.
doi: https://doi.org/10.14456/nujst.2018.10.