Notice that instead of the symmedian point one could select some other arbitrary point K' and consider the projectivity fixing the vertices and sending K' to D. In that case each circumconic would be the image of the conic defined through the point K'. By selecting though K we arive at obtaining each circumconic as the image of the

By selecting the K' to be the centroid G we get all circumconics as images of the outer Steiner ellipse of triangle ABC. The arguments at the end of ProjectivityFixingVertices.html show also the locations of D for which the corresponding conic is an ellipse, parabola or hyperbola. It is correspondingly the inner/on/outside of the inner Steiner ellipse of ABC.

A slightly different method to obtain all conics through

ProjectivityFixingVertices.html

Steiner_Ellipse.html

TriangleCircumconics2.html

TriangleConics.html

TriangleProjectivitiesPlay.html

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