This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

2019 Moroccan TST, 2
Tags: morocco , inequalities
Let $a>1$ be a real number. Prove that for all $n\in\mathbb{N}*$ that : $\frac{a^n-1}{n}\ge \sqrt{a}^{n+1}-\sqrt{a}^{n-1}$

2019 Moroccan TST, 1
Tags: geometry , morocco
Let $ABCD$ a cyclique quadrilateral. We consider the Following points: $A'$ the orthogonal projection of $A$ over $(BD)$, $B'$ the orthogonal projection of $B$ over $(AC)$, $C'$ the orthgonal projection of $C$ over $(BD)$ and $D'$ being the orthogonal projection of $D$ over $(AC)$ Prove that $A', B', C'$ and $D'$.