List questions from geometric-inequalities

Published on 13 Apr 2026 - 14:50

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How to prove $\cos(\frac{B-C}2)\ge \sqrt{\frac{2r}{R}}$?

Published on 12 Apr 2026 - 14:03

156

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How prove this $\frac{r}{R}\ge\frac{AM}{AX}$

Published on 10 Apr 2026 - 19:40

147

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A geometric inequality

Published on 15 Apr 2026 - 9:02

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How prove $\sum\limits_{cyc}\sqrt{PA+PB}\ge 2\sqrt{\sum\limits_{cyc}h_{a}}$

Published on 10 Apr 2026 - 23:42

366

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How prove this $S_{\Delta ABC}\ge\frac{3\sqrt{3}}{4\pi}$

Published on 13 Apr 2026 - 20:38

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Prove sum of distance from triangle vertices to a point inside triangle is more than semiperimeter and less than perimeter

Published on 14 Apr 2026 - 3:51

3.6k

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Alternate proof for $a^2+b^2+c^2\le 9R^2$

Published on 14 Apr 2026 - 2:16

3.1k

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Greatest value of $|z|$ such that $|z-2i|\le2$ and $ 0\le \arg(z+2)\le 45^\circ$

Published on 14 Apr 2026 - 1:45

350

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Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$

Published on 15 Apr 2026 - 8:43

82

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How prove $ \frac{2}{\sqrt3}F \geq s-1 $ for convex quadrilateral?

Published on 14 Apr 2026 - 18:31

141

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Prove the following triangle related inequality

Published on 15 Apr 2026 - 14:17

68

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Inequality $a^2+4b^2<1$.

Published on 13 Apr 2026 - 23:10

58

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$(1+x)^r \le 2^{r-1} + 2^{r-1}x^r, x>0,r>1.$

Published on 15 Apr 2026 - 16:12

42

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in an given inequality prove that all sides are equal

Published on 26 Mar 2026 - 4:52

List Question

Proving a tough geometrical inequality, with equality in equilateral triangles.

How to prove $\cos(\frac{B-C}2)\ge \sqrt{\frac{2r}{R}}$?

How prove this $\frac{r}{R}\ge\frac{AM}{AX}$

A geometric inequality

How prove $\sum\limits_{cyc}\sqrt{PA+PB}\ge 2\sqrt{\sum\limits_{cyc}h_{a}}$

How prove this $S_{\Delta ABC}\ge\frac{3\sqrt{3}}{4\pi}$

Prove sum of distance from triangle vertices to a point inside triangle is more than semiperimeter and less than perimeter

Alternate proof for $a^2+b^2+c^2\le 9R^2$

Greatest value of $|z|$ such that $|z-2i|\le2$ and $ 0\le \arg(z+2)\le 45^\circ$

Given $a,b,c$ are the sides of a triangle. Prove that $\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}<2$

How prove $ \frac{2}{\sqrt3}F \geq s-1 $ for convex quadrilateral?

Prove the following triangle related inequality

Inequality $a^2+4b^2<1$.

$(1+x)^r \le 2^{r-1} + 2^{r-1}x^r, x>0,r>1.$

in an given inequality prove that all sides are equal

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