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  "body": "\n## Summary\n\nThe Fermat point of a [[triangle|0CTNFGYMM2]] is the point of the plane whose total distance to the three vertices is as small as possible.\nWhen every angle of the triangle is less than $120^\\circ$, it is the interior point that sees each side under $120^\\circ$.\nIt is a model case of a geometric minimisation problem and of a [[triangle center|WRKFH25NCX]].\n\n## Explanations\n\n### L1 human\n\nThree villages want to build one meeting point and join it to each village by a straight road.\nThe Fermat point is the place that makes the total length of road as short as possible.\nAt this point the three roads meet at equal angles of $120^\\circ$, unless one corner of the triangle is already very blunt.\nFor an equilateral triangle the Fermat point is simply the centre.\n",
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