Darboux cubic (K004)
Here again we construct a triangle and after that Darboux cubic for this triangle. Then we take point on the cubic and after that we cojugate this point isogonal, we get another point on the same cubic. By using GeoGebra we come to the conlusion that Darboux cubic is isogonal transform of itself.
Barycentric equation
Proof
Here we substitude , and in the same way as that in the previous cubics
And again we have the same equation as that in the beginning. darboux cubic is isogonal transform of itself.