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

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Found problems: 2

2021 Vietnam National Olympiad, 2
Find all function $f:\mathbb{R}\to \mathbb{R}$ such that \[f(x)f(y)=f(xy-1)+yf(x)+xf(y)\] for all $x,y \in \mathbb{R}$
function national olympiads functional equation algebra functional equations mathematical induction

2015 Canada National Olympiad, 4
Let $ABC$ be an acute-angled triangle with circumcenter $O$. Let $I$ be a circle with center on the altitude from $A$ in $ABC$, passing through vertex $A$ and points $P$ and $Q$ on sides $AB$ and $AC$. Assume that \[BP\cdot CQ = AP\cdot AQ.\] Prove that $I$ is tangent to the circumcircle of triangle $BOC$.
national olympiads circumcircle geometry angle chasing construction cyclic quadrilaterals homothety power of a point spiral similarity symmedians