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

1952 Moscow Mathematical Olympiad, 214
Prove that if $|x| < 1$ and $|y| < 1$, then $\left|\frac{x - y}{1 -xy}\right|< 1$.
inequalities moscow absolute value algebra

2015 Oral Moscow Geometry Olympiad, 5
A triangle $ABC$ and spheres are given in space $S_1$ and $S_2$, each of which passes through points $A, B$ and $C$. For points $M$ spheres $S_1$ not lying in the plane of triangle $ABC$ are drawn lines $MA, MB$ and $MC$, intersecting the sphere $S_2$ for the second time at points $A_1,B_1$ and $C_1$, respectively. Prove that the planes passing through points $A_1, B_1$ and $C_1$, touch a fixed sphere or pass through a fixed point.
moscow geometry 3d geometry fixed point plane sphere solid geometry