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: 3

2018 Greece Team Selection Test, 2
Tags: power of point , homothety , geometry
A triangle $ABC$ is inscribed in a circle $(C)$ .Let $G$ the centroid of $\triangle ABC$ . We draw the altitudes $AD,BE,CF$ of the given triangle .Rays $AG$ and $GD$ meet (C) at $M$ and $N$.Prove that points $ F,E,M,N $ are concyclic.

2016 Saint Petersburg Mathematical Olympiad, 5
Tags: power of point , coaxial circles , circumcircle , geometry
Points $A$ and $P$ are marked in the plane not lying on the line $\ell$. For all right triangles $ABC$ with hypotenuse on $\ell$, show that the circumcircle of triangle $BPC$ passes through a fixed point other than $P$.

2018 Greece Team Selection Test, 2
Tags: homothety , geometry , power of point
A triangle $ABC$ is inscribed in a circle $(C)$ .Let $G$ the centroid of $\triangle ABC$ . We draw the altitudes $AD,BE,CF$ of the given triangle .Rays $AG$ and $GD$ meet (C) at $M$ and $N$.Prove that points $ F,E,M,N $ are concyclic.