List questions from geometric-inequalities

Published on 09 Apr 2026 - 18:59

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Intersection of interlaced periodic intervals

Published on 12 Apr 2026 - 0:46

161

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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 14 Apr 2026 - 6:34

483

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Inequality on outer product

Published on 10 May 2026 - 12:49

286

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

Published on 16 Apr 2026 - 2:40

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An inequality with sides of a triangle

Published on 10 May 2026 - 18:26

384

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tangent inequality in triangle

Published on 10 May 2026 - 19:56

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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 15 Apr 2026 - 3:55

135

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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 16 Apr 2026 - 14:16

74

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

Published on 11 Apr 2026 - 21:17

113

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

Published on 15 Apr 2026 - 17:58

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Sides of a quadrilateral

Published on 10 May 2026 - 22:07

181

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

Published on 10 Apr 2026 - 18:48

71

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Calculate the inequality

Published on 30 Apr 2026 - 13:39

436

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

Published on 15 Apr 2026 - 13:12

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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