List questions from geometric-inequalities

Published on 16 Jul 2019 - 11:01

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Intersection of interlaced periodic intervals

Published on 19 Jul 2019 - 10:49

158

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Two rectangles are inscribed in acute triangle; maximize the ratio of their area to the triangle's area, or show there is no maximum

Published on 21 Jul 2019 - 18:24

479

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Inequality on outer product

Published on 31 Jul 2019 - 19:44

283

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Find the minimal value the hypotenuse of a right triangle whose radius of inscribed circle is $r$

Published on 02 Aug 2019 - 22:41

49

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An inequality with sides of a triangle

Published on 25 Mar 2026 - 7:43

381

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tangent inequality in triangle

Published on 25 Mar 2026 - 9:46

124

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If $a, b, c$ are the sidelengths of a triangle, show that $a^2b(a−b) +b^2c(b−c)+c^2a(c−a)\ge0$.

Published on 23 Aug 2019 - 12:19

132

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If $a$, $b$, $c$ are sides of a triangle, prove $2(a+b+c)(a^2+b^2+c^2)\geq3(a^3+b^3+c^3+3abc)$

Published on 06 Sep 2019 - 5:14

71

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How to prove that a point defined by trigonometric functions involving 4 parameters is inside a certain tetrahedron?

Published on 12 Sep 2019 - 21:23

110

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$\sum_{cyclic}\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}\leq 3$

Published on 28 Sep 2019 - 7:02

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Sides of a quadrilateral

Published on 25 Mar 2026 - 17:24

178

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How find the $AP+\frac{1}{2}BP$ minmum value

Published on 21 Apr 2014 - 10:44

67

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Calculate the inequality

Published on 30 Apr 2014 - 5:42

433

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A geometric inequality, proving $8r+2R\le AM_1+BM_2+CM_3\le 6R$

Published on 06 May 2014 - 7:00

List Question

How do I prove the minimum for given trigonometric expression of two angles

Intersection of interlaced periodic intervals

Two rectangles are inscribed in acute triangle; maximize the ratio of their area to the triangle's area, or show there is no maximum

Inequality on outer product

Find the minimal value the hypotenuse of a right triangle whose radius of inscribed circle is $r$

An inequality with sides of a triangle

tangent inequality in triangle

If $a, b, c$ are the sidelengths of a triangle, show that $a^2b(a−b) +b^2c(b−c)+c^2a(c−a)\ge0$.

If $a$, $b$, $c$ are sides of a triangle, prove $2(a+b+c)(a^2+b^2+c^2)\geq3(a^3+b^3+c^3+3abc)$

How to prove that a point defined by trigonometric functions involving 4 parameters is inside a certain tetrahedron?

$\sum_{cyclic}\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}\leq 3$

Sides of a quadrilateral

How find the $AP+\frac{1}{2}BP$ minmum value

Calculate the inequality

A geometric inequality, proving $8r+2R\le AM_1+BM_2+CM_3\le 6R$

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