List questions from geometric-inequalities

Published on 18 Oct 2013 - 11:39

381

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An inequality for sides of a triangle

Published on 18 Feb 2014 - 23:03

175

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Prove $8(1-\cos^2a)(1-\cos^2b)(1-\cos^2c) \geq 27 \cos a\cos b\cos c$

Published on 11 Apr 2017 - 3:21

92

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minimum value of $3$ square root function of variables $x,y$

Published on 15 Apr 2017 - 2:58

83

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In $\triangle ABC$, $|PA| \le |PB| + |PC|$

Published on 16 Apr 2017 - 13:16

516

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The concept/physical meaning/interpretations behind the Bessel's inequality

Published on 17 Apr 2017 - 10:21

142

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Algebra: Prove inequality $\frac{ab + bc + ca}{4S}\ge \operatorname{ctg} \frac{\pi}{6}$

Published on 02 May 2017 - 11:00

126

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The sides $a$, $b$, $c$ of a triangle with area $D$ are such that $ab+bc+ca\ge 4\sqrt{3}D$

Published on 03 May 2017 - 7:10

79

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A geometric inequality concerning angles

Published on 05 May 2017 - 21:14

136

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Prove that semi-perimeter $\geq a \cos A+b \cos B+c \cos C $

Published on 26 Mar 2026 - 13:01

239

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Given $a+b+c+d=4$ To find Minimum value of $\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}$

Published on 11 May 2017 - 2:32

265

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Prove: $\frac{a}{m_a}+\frac{b}{m_b}+\frac{c}{m_c}\ge 2\sqrt{3}$

Published on 26 Mar 2026 - 19:18

137

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Find minimum and maximum of $\frac {m_a}{b+c}+\frac {m_b}{c+a}+ \frac {m_c}{a+b} $

Published on 13 May 2017 - 12:20

47

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Trigonometry+inequality.

Published on 21 May 2017 - 8:13

70

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How to prove this geometry inequality dealing with area of triangles inscribed in a same circle？

Published on 31 May 2017 - 4:14

List Question

How find this maximum $S_{\Delta ABC}$

An inequality for sides of a triangle

Prove $8(1-\cos^2a)(1-\cos^2b)(1-\cos^2c) \geq 27 \cos a\cos b\cos c$

minimum value of $3$ square root function of variables $x,y$

In $\triangle ABC$, $|PA| \le |PB| + |PC|$

The concept/physical meaning/interpretations behind the Bessel's inequality

Algebra: Prove inequality $\frac{ab + bc + ca}{4S}\ge \operatorname{ctg} \frac{\pi}{6}$

The sides $a$, $b$, $c$ of a triangle with area $D$ are such that $ab+bc+ca\ge 4\sqrt{3}D$

A geometric inequality concerning angles

Prove that semi-perimeter $\geq a \cos A+b \cos B+c \cos C $

Given $a+b+c+d=4$ To find Minimum value of $\frac{a}{b^3+4}+\frac{b}{c^3+4}+\frac{c}{d^3+4}+\frac{d}{a^3+4}$

Prove: $\frac{a}{m_a}+\frac{b}{m_b}+\frac{c}{m_c}\ge 2\sqrt{3}$

Find minimum and maximum of $\frac {m_a}{b+c}+\frac {m_b}{c+a}+ \frac {m_c}{a+b} $

Trigonometry+inequality.

How to prove this geometry inequality dealing with area of triangles inscribed in a same circle？

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