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  "body": "\n## Summary\n\nLet $P$ be a point on the [[circumcircle|03VZJE6C8C]] of a [[triangle|0CTNFGYMM2]].\nIts Simson line is the line through the feet of the perpendiculars from $P$ to the three side lines.\nThese three feet are [[collinear|0AFNNTRTJE]] exactly when $P$ lies on the circumcircle.\nThe Simson line is a basic object of triangle geometry and appears in many angle chasing arguments.\n\n## Explanations\n\n### L1 human\n\nPick a point on the circle through the three corners of a triangle.\nDrop a perpendicular from it to each of the three sides, extended if needed.\nThe three feet of these perpendiculars always lie on one straight line.\nFor example, if the point is a corner $A$, two of the feet are $A$ itself, and the line is the altitude from $A$.\n",
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