A particular case of quadratic transformation is the

Here we show that the isogonal transformation of ABC coincides with the quadratic transformation of a special family of conics consisting entirely of rectangular hyperbolas. The family namely consists of all conics passing through the four intersection points {I,A',B',C'} of the bisectors of the triangle. All these conics are rectangular hyperbolas. Their family is generated by the linear combinations of two degenerate members c

The proof, modulo the remarks made above, is trivial. Apply the definition of the quadratic transformation by taking the polars of P with respect to c

Although the property has a simple proof. The context involves several interesting ideas studied in the references given below.

Isogonal_Conjugation.html

IsotomicAsQuadratic.html

Quadratic_Transformation.html

Quadratic_Transformation2.html

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