The intersection point I of line BD and the tangent t

Conic c' is bitangent to c at points D and C (see BitangentConics.html ).

The proof reduces to a trivial property of equilateral hyperbolas (see HyperbolaRelatedToEquilateral.html ).

This is done by defining a homography which maps the conic c to a circle c

Such a homography is easily constructed by coordinates-correspondence with respect to self polar triangles, and taking one of the sides of the autopolar triangle to pass through A.

Draw from A lines intersecting the conic at points BB' and construct the locus-conic (d) of the previous section. The intersection points {D

DD

See the file TrianglesGivenPivotCanonical.html for a special construction along these lines.

In fact, given a point A on the circle and its tangent there, consider another point B variable on the circle and draw from there the parallel BC to the tangent, C being the other intersection point of this parallel with the circle. The tangent t

HyperbolaRelatedToEquilateral.html

TrianglesGivenPivotCanonical.html

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