New posts in Geometric Inequalities

Does this strong convexity estimate hold?

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

Proving a complicated looking inequality in a simple way

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

Prove that $m_a\geq \dfrac{b^2+c^2}{4R}$

A bound for $\sqrt\frac{b+c-a}a+\sqrt\frac{c+a-b}b+\sqrt\frac{a+b-c}c$ in a triangle

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

tangent inequality in triangle

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

In an equilateral triangle, prove that $|BQ| + |PQ| + |CP| > 2l$