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  "body": "\n## Summary\n\nInversive geometry studies the plane with one point at infinity added.\nIt keeps the properties of figures that are preserved by inversions in circles and reflections in lines.\nIn it, lines count as circles through the point at infinity, and inversions map circles to circles.\nIts transformations are the Möbius transformations and their composites with complex conjugation.\nSo it is the geometry of the Riemann sphere in the sense of the Erlangen program.\n\n## Explanations\n\n### L1 human\n\nInversive geometry treats lines and circles alike: a line is a circle that passes through a point at infinity.\nIts basic moves are reflections in lines and inversions in circles, which turn circles into circles and keep angles between curves.\nLengths and straightness are not kept, so problems about tangent circles can often be simplified by an inversion that turns some circles into lines.\nFor example, two circles touching at a point $P$ become two parallel lines after an inversion centered at $P$.\n",
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