List questions from geometric-inequalities

Published on 25 Aug 2016 - 23:20

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A beautiful triangle inequality

Published on 28 Aug 2016 - 17:58

119

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Range of $\tan^2\frac A2+\tan^2\frac B2+\tan^2 \frac C2$ with $A,B,C$ angles in a triangle

Published on 25 Mar 2026 - 21:50

78

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The inequality $p<\frac{a+m_b}{b+m_a}<q$

Published on 05 Sep 2016 - 15:59

1k

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prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$

Published on 26 Mar 2026 - 1:23

211

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Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

Published on 16 Sep 2016 - 13:55

133

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Showing inequality $\tan{A}\tan{B}\tan{C}\ge 8$

Published on 16 Sep 2016 - 15:00

43

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Proving a difficult inequality involving orthonormal vectors of $\mathbb{R}^4$

Published on 02 Oct 2016 - 9:59

2k

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Unit square inside triangle.

Published on 04 Oct 2016 - 13:50

64

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The Proof Of Basic Inequalities

Published on 16 Oct 2016 - 13:22

207

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Cauchy Schwarz inequality on $V \wedge V $

Published on 19 Oct 2016 - 14:41

37

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If $m_a$ be the length of the median on side $a$ of acute angled triangle $ABC$ then $(m_a)^2 \le 2b^2c^2(1+\cos A)$..

Published on 26 Oct 2016 - 16:19

70

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An inequality involving $n$ blue points and $n$ red points on a line.

Published on 02 Nov 2016 - 8:10

210

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Prove that $\triangle ABC$ is equilateral, If $(a+b-c)^{a}\cdot (b+c-a)^{b}\cdot (c+a-b)^{c}\geq a^a\cdot b^b\cdot c^c$

Published on 25 Mar 2026 - 9:28

67

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Find the tightest upper bound of $\sum\limits_{j = 1}^n v_j^2 w_j \leq C\sum\limits_{j = 1}^n v_j^2$

Published on 21 Nov 2016 - 3:52

List Question

If $a$, $b$, and $c$ are sides of a triangle, then $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$.

A beautiful triangle inequality

Range of $\tan^2\frac A2+\tan^2\frac B2+\tan^2 \frac C2$ with $A,B,C$ angles in a triangle

The inequality $p<\frac{a+m_b}{b+m_a}<q$

prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$

Prove the inequality $\sqrt{a^2+b^2}+\sqrt{c^2+b^2}+\sqrt{a^2+c^2}<1+\frac{\sqrt2}{2}$

Showing inequality $\tan{A}\tan{B}\tan{C}\ge 8$

Proving a difficult inequality involving orthonormal vectors of $\mathbb{R}^4$

Unit square inside triangle.

The Proof Of Basic Inequalities

Cauchy Schwarz inequality on $V \wedge V $

If $m_a$ be the length of the median on side $a$ of acute angled triangle $ABC$ then $(m_a)^2 \le 2b^2c^2(1+\cos A)$..

An inequality involving $n$ blue points and $n$ red points on a line.

Prove that $\triangle ABC$ is equilateral, If $(a+b-c)^{a}\cdot (b+c-a)^{b}\cdot (c+a-b)^{c}\geq a^a\cdot b^b\cdot c^c$

Find the tightest upper bound of $\sum\limits_{j = 1}^n v_j^2 w_j \leq C\sum\limits_{j = 1}^n v_j^2$

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