Napoleon cubic (K005)
We construct triangle and Napolen cubic for this triangle. After that we take point on the cubic and then we cojugate that point isogonal we get point which is also on the Napoleon cubic. And by using GeoGebra we conclude that Napoleon cubic is isogonal transform of itself.
Barycentric equation
Here we again substitude , and with , and .
And again we have the same equation as that in the beginning. Napoleon cubic is isogonal transform of itself.