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  "body": "\n## Summary\n\nAn orthocentric system is a set of four points of the plane.\nIn it, one point is the [[orthocentre|0WB619CA0V]] of the triangle formed by the other three.\nThen each of the four points is the orthocentre of the triangle formed by the other three.\nThe four triangles share the same [[nine-point circle|033H8MQRC3]], and their circumcircles all have the same radius.\n\n## Explanations\n\n### L1 human\n\nTake a triangle that has no right angle and mark its orthocentre, where the altitudes meet.\nNow you have four points.\nPick any three of them: their orthocentre is the fourth point.\nSo the four points play symmetric roles, and none of them is special.\nFor example, $(0, 2)$, $(-1, 0)$, $(1, 0)$ and $(0, \\frac{1}{2})$ form such a system.\n",
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