New posts in geometric-inequalities

Given three a-triangle-sidelengths $a,b,c$. Prove that $3\left((a^{2}b(a-b)+b^{2}c(b-c)+c^{2}a(c-a)\right)\geqq b(a+b-c)(a-c)(c-b)$ .

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An inequality about the sum of distances between points : same color $\le$ different colors?

inequality summation euclidean-geometry geometric-inequalities

Geometric inequality $\frac{R_a}{2a+b}+\frac{R_b}{2b+c}+\frac{R_c}{2c+a}\geq\frac{1}{\sqrt3}$

geometry inequality contest-math geometric-inequalities

The inequality $\frac{MA}{BC}+\frac{MB}{CA}+\frac{MC}{AB}\geq \sqrt{3}$

geometry inequality triangles geometric-inequalities

Extreme of $\cos A\cos B\cos C$ in a triangle without calculus.

trigonometry inequality optimization geometric-inequalities

Let $a$, $b$ and $c$ be the three sides of a triangle. Show that $\frac{a}{b+c-a}+\frac{b}{c+a-b} + \frac{c}{a+b-c}\geqslant3$.

inequality contest-math euclidean-geometry triangles geometric-inequalities

How to prove that $ \sin \angle{GAB}+\sin \angle{GBC}+\sin \angle{GCA} \le \frac{3}{2} $ for a triangle $ABC$ with centroid $G$?

geometry trigonometry inequality geometric-inequalities

How prove this geometry inequality $R_1^4+R_2^4+R_3^4+R_4^4+R_5^4\geq {4\over 5\sin^2 108^\circ}S^2$

geometry inequality contest-math geometric-inequalities