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.

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Found problems: 2

2025 Sharygin Geometry Olympiad, 15
Tags: geometry , Sharygin Geometry Olympiad , Trignometry , tangent circles
A point $C$ lies on the bisector of an acute angle with vertex $S$. Let $P$, $Q$ be the projections of $C$ to the sidelines of the angle. The circle centered at $C$ with radius $PQ$ meets the sidelines at points $A$ and $B$ such that $SA\ne SB$. Prove that the circle with center $A$ touching $SB$ and the circle with center $B$ touching $SA$ are tangent. Proposed by: A.Zaslavsky

2022 239 Open Mathematical Olympiad, 8
Tags: algebra , number theory , Trignometry
Prove that there is positive integers $N$ such that the equation $$arctan(N)=\sum_{i=1}^{2020} a_i arctan(i),$$ does not hold for any integers $a_{i}.$