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: 26

2023 Brazil EGMO Team Selection Test, 1
Tags: circumcircle , geometry , orthocenter , circumcenter , euler circle
Let $\Delta ABC$ be a triangle with orthocenter $H$ and $\Gamma$ be the circumcircle of $\Delta ABC$ with center $O$. Consider $N$ the center of the circle that passes through the feet of the heights of $\Delta ABC$ and $P$ the intersection of the line $AN$ with the circle $\Gamma$. Suppose that the line $AP$ is perpendicular to the line $OH$. Prove that $P$ belongs to the reflection of the line $OH$ by the line $BC$.