Projective Geometry Preset empty plane conic sections focal points conic pencils dual conic pencils complete quadrangle conic sections 1 conic sections 2 pencil of conics dual pencil of conics pencil of circles pencil of horocycles Desargues' theorem Pappus' theorem Pascal's theorem Brianchon's (dual of Pascal's) three-conics theorem focal quadrangles circumferences incircles and excircles circles by line&points circles by point&lines nine-point conic (Euclidean) Feuerbach circle (Euclidean) gardener's ellipse focus-sharing ellipses Metric +++|+++ 00+|++0 ++−|++− ++0|00+ 00+|+00 0+−|+00 −++|−++ 00+|+−0 +−+|+−+ elliptic Euclidean hyp: Lobachevskian dual Euclidean Galilean dual Minkowskian hyp: dual Lobachevskian Minkowskian hyp: de Sitter Elementary constructions draggable points intersections of lines/conics midpoints of a pair of points focal points of a pair of conics draggable lines lines given points/tangent conics angular or perpendicular bisectors perpendicular to a line focal lines of a pair of conics conics given points/tangents singular conic conic given a focal pair to a conic element of a pencil of conics circle given center and periphery circles given points/tangents poles/polars to a conic images under a reflection tangents of a conic pencil of conics dual pencil of conics hide objects reveal hidden objects
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