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Special Triangles

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Recent Advances in Geometric Inequalities

Part of the book series: Mathematics and Its Applications ((MAEE,volume 28))

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Abstract

If for a triangle ABC with sides a, b, c and circumradius R the equation a2 + b2 + c2 = 9R2 holds, the triangle is equilateral. Each triangle satisfying a2 + b2 + c2 = 8R2 is a right triangle. Starting from these well-known properties V. Devidé [1] has investigated at length the special class of triangles defined by a2 + b2 + c2 = 6R2. O. Bottema [2] considered the general class of triangles (k-triangles) defined by a2 + b2 + c2 = kR2. In [12] it has been shown that a2 + b2 + c2 = 5R2 characterizes all the triangles for which the nine-point centre lies on the circumcircle.

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Authors and Affiliations

  1. University of Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Yugoslavia

    J. E. Pečarić & V. Volenec

Authors
  1. D. S. Mitrinović
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  2. J. E. Pečarić
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  3. V. Volenec
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© 1989 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Volenec, V. (1989). Special Triangles. In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_10

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  • DOI: https://doi.org/10.1007/978-94-015-7842-4_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8442-2

  • Online ISBN: 978-94-015-7842-4

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