[1] Conic c can be obtained as the image of the circumcircle of the equilateral A

[2] The conic c can be elliptic, parabolic or hyperbolic, depending on the shape of the triangle. Its focal points Z

[3] Line f is orthogonal to L (called the

[4] Line L coincides with the

[5] Line f carries several triangle centers. For example: the De Longchamps point X(20), X(77), X(170), X(269), X(279), X(347), X(357), X(358), X(390).

[6] Consider another equilateral A

[6.1] Same incircle, and conjugate conic, same Gergonne point G, incenter I, lines f and L.

[6.2] Triangle centers of A'B'C' lying on f either remain the same or move on line f. In particular the Soddy points of all triangles A'B'C' are the same.

[6.3] Triangle centers of A'B'C' lying on L either remain fixed or move on line L.

[7] The circumcenters of A'B'C' describe another conic c', not belonging to the family generated by the incircle and its conjugate conic c, sharing though with c one axis.

CrossRatio.html

CrossRatio0.html

CrossRatioLines.html

GoodParametrization.html

Harmonic.html

Harmonic_Bundle.html

HomographicRelation.html

HomographicRelationExample.html

Pascal.html

PascalOnTriangles.html

ProjectivityFixingVertices.html

ProjectiveRotations.html

Steiner_Ellipse.html

TriangleCircumconics.html

TriangleCircumconics2.html

TriangleConics.html

TriangleProjectivitiesPlay.html

TrilinearPolar.html

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