All Questions

Let $ABCD$ be a convex quadrilateral with the lengths $a, b, c, d$ and the area $S$. The main result in our paper equivalent to: \begin{equation} a^2+b^2+c^2+d^2 \ge 4S + \frac{\sqrt{3}-1}{\sqrt{3}}\...

Let $n$-regular polygon $X_1X_2\cdots X_n$ with the circumcribed circle $(O)$. Let $n$ points $A_1, A_2,\cdots,A_n$ lie on the circle $(O)$. Let $x_{ij}=X_iX_j$ (for $1 \le i<j \le n) $. Let $a_{ij}...