List questions from geometric-inequalities

Published on 14 Apr 2026 - 7:43

378

Views

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 16 Apr 2026 - 2:40

78

Views

Geometric inequality in triangle with inradius

Published on 11 Apr 2026 - 12:05

359

Views

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

Published on 18 Apr 2026 - 5:38

103

Views

Law of Cosines and Heron's Formula in inequalities

Published on 14 Apr 2026 - 3:06

214

Views

Inequality involving the angle bisectors of a triangle

Published on 10 May 2026 - 17:15

162

Views

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

Published on 11 May 2026 - 1:47

49

Views

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 16 Apr 2026 - 22:03

61

Views

Proofs: Relationships in Triangles

Published on 12 Apr 2026 - 1:45

135

Views

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 09 Apr 2026 - 7:32

720

Views

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 10 May 2026 - 19:40

171

Views

Proving a complicated looking inequality in a simple way

Published on 12 Apr 2026 - 20:09

171

Views

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

Published on 14 Apr 2026 - 16:46

53

Views

Parallelepiped inequality and probabilistic proof

Published on 14 Apr 2026 - 21:31

336

Views

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

Published on 11 Apr 2026 - 22:20

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

Trending Questions

Popular # Hahtags

Popular Questions