[size=85]Here again we have same construcyion but for Simson cubic. By using GeoGebra we conclude that Simson cubic is isogonal transform of K(162). [/size]

[math]\sum_{cyclic} a^2\frac{y+z}{y-z}=0[/math][br][math]\sum_{cyclic}S_Ax\left(y^2+z^2\right)-\left(a^2+b^2+c^2\right)xyz[/math]

[size=85]We again substitude [math]x[/math], [math]y[/math] and [math]z[/math] with [br][math]\sum_{cyclic}S_Ax\left(y^2+z^2\right)-\left(a^2+b^2+c^2\right)xyz[/math][br][math]\sum_{cyclic}S_Aa^2yz\left(b^4x^2z^2-c^4x^2y^2\right)-\left(a^2+b^2+c^2\right)a^2yzb^2xzc^2yx[/math][br][math]x^2y^2z^2\sum_{cyclic}a^2S_Ax\left(c^4y^2+b^4z^2\right)-a^2b^2c^2\left(a^2+b^2+c^2\right)xyz[/math][br]And this is the equation of the K162 cubic which means that Simson cubic is isogonal transform of K162.[/size][br][br][br][br]