Missouri Journal of Mathematical Sciences

Generalization of a Geometric Inequality

Xiao-Guang Chu and Jian Liu

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Abstract

In this paper, using Bottema's inequality for two triangles and other results, the generalization of an inequality involving the medians and angle-bisectors of the triangle is proved. This settles affirmatively a problem posed by J-Liu.

Article information

Source
Missouri J. Math. Sci. Volume 21, Issue 3 (2009), 155-162.

Dates
First available: 14 September 2011

Permanent link to this document
http://projecteuclid.org/euclid.mjms/1316024881

Mathematical Reviews number (MathSciNet)
MR2584541

Zentralblatt MATH identifier
1187.51016

Subjects
Primary: 51M16: Inequalities and extremum problems {For convex problems, see 52A40}

Citation

Chu, Xiao-Guang; Liu, Jian. Generalization of a Geometric Inequality. Missouri Journal of Mathematical Sciences 21 (2009), no. 3, 155--162. http://projecteuclid.org/euclid.mjms/1316024881.


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References

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  • J.-Liu, Some New Inequalities for the Triangle, Zhongxue Shuxue, 5 (1994), 9–12 (Chinese).
  • J.-P. Li, A Proof of a Conjecture, Hunan Mathematical Communication, 2 (1995), 39–40 (Chinese).
  • X.-Zh. Yang, A Inequality of the Bisector, Shuxue Tongxun, 8 (1995), 17 (Chinese).
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  • D. Mitrinović, J. E. Pečarić, and V. Volenec, Recent Advances in Geometric Inequalities, Kluwer Academic Publishers, Dordrecht, Netherlands, 1989.
  • O. Bottema, Hoofdstukken uit de Elementaire Meetkunde, Den Haag, (1944), 97–99.