List questions from geometric-inequalities

Published on 20 Mar 2020 - 11:07

375

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the sum of the reciprocals of the lengths of the interior angle bisectors of a triangle and the sum of the reciprocals of the lengths of the sides

Published on 26 Mar 2020 - 19:13

75

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Geometric inequality in triangle with inradius

Published on 28 Mar 2020 - 1:31

356

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For acute $\triangle ABC$, prove $(\cos A+\cos B)^2+(\cos A+\cos C)^2+(\cos B+\cos C)^2\leq3$

Published on 28 Mar 2020 - 18:42

100

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Law of Cosines and Heron's Formula in inequalities

Published on 31 Mar 2020 - 4:20

211

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Inequality involving the angle bisectors of a triangle

Published on 25 Mar 2026 - 9:38

161

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Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$

Published on 25 Mar 2026 - 12:55

46

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Prove that : $\prod_{cyc}(2a^2+2b^2-c^2)\prod_{cyc}(a+b-c)\leq a^2b^2c^2(a+b+c)^3$

Published on 02 Apr 2020 - 14:56

58

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Proofs: Relationships in Triangles

Published on 10 Apr 2020 - 3:56

134

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Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

Published on 23 Feb 2026 - 2:50

719

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If $a,b,c$ are the sides of a triangle, then $\dfrac{a}{b+c-a}+\dfrac{b}{c+a-b}+\dfrac{c}{a+b-c}$ is:

Published on 25 Mar 2026 - 12:41

168

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Proving a complicated looking inequality in a simple way

Published on 17 Apr 2020 - 9:26

168

Views

Minimize $|a-1|^3+|b-1|^3$ with constant product $ab=s$

Published on 19 Apr 2020 - 12:53

50

Views

Parallelepiped inequality and probabilistic proof

Published on 20 Apr 2020 - 19:38

333

Views

If the side lengths of a triangle increase and the third side is fixed, the opposite angle decreases

Published on 22 Apr 2020 - 10:21

List Question

The maximum for $xy \sin \alpha + yz \sin \beta +zx \sin \gamma$.

the sum of the reciprocals of the lengths of the interior angle bisectors of a triangle and the sum of the reciprocals of the lengths of the sides

Geometric inequality in triangle with inradius

For acute $\triangle ABC$, prove $(\cos A+\cos B)^2+(\cos A+\cos C)^2+(\cos B+\cos C)^2\leq3$

Law of Cosines and Heron's Formula in inequalities

Inequality involving the angle bisectors of a triangle

Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$

Prove that : $\prod_{cyc}(2a^2+2b^2-c^2)\prod_{cyc}(a+b-c)\leq a^2b^2c^2(a+b+c)^3$

Proofs: Relationships in Triangles

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

If $a,b,c$ are the sides of a triangle, then $\dfrac{a}{b+c-a}+\dfrac{b}{c+a-b}+\dfrac{c}{a+b-c}$ is:

Proving a complicated looking inequality in a simple way

Minimize $|a-1|^3+|b-1|^3$ with constant product $ab=s$

Parallelepiped inequality and probabilistic proof

If the side lengths of a triangle increase and the third side is fixed, the opposite angle decreases

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