[size=85]Here we have the same construction as that in the previous one but here we construct Lemoine cubic.By using GeoGebra we conclude that Lemoine cubic is isogonal transformed of K028.[/size]

[math]\sum_{cyclic} a^4\left(b^2+c^2-a^2\right)yz\left(y-z\right)+2\left(a^2^{ }-b^2\right)\left(b^2-c^2\right)\left(c^2-a^2\right)xyz[/math]

We again substitude [math]x[/math], [math]y[/math] and [math]z[/math] with [math]a^2zy[/math], [math]b^2xz[/math] and [math]z^2xy[/math].[br][math]\sum_{cyclic} a^4\left(b^2+c^2-a^2\right)yz\left(y-z\right)+2\left(a^2^{ }-b^2\right)\left(b^2-c^2\right)\left(c^2-a^2\right)xyz[/math][br][math]\sum_{cyclic}a^4\left(b^2+c^2-a^2\right)b^2xzc^2xy\left(b^2xz-c^2xy\right)+\left(2\prod_{cyclic}\left(b^2-c^2\right)\right)a^2b^2c^2x^2y^2z^2[/math][br][math]\sum_{cyclic}a^2S_Ax^2\left(b^2z-c^2y\right)+\left(2\prod_{cyclic}\left(b^2-c^2\right)\right)xyz=0[/math] [br][math]\sum_{cyclic}a^2S_Ax^2\left(b^2z-c^2y\right)=a^2S_Ax^2\left(b^2^{ }z-c^2y\right)+b^2S_By^{2^{ }}\left(c^{2^{ }}x-a^2z\right)+c^2S_Cz^2\left(a^2y-b^2x\right)[/math][br][br][math]\sum_{cyclic}b^2c^2x\left(S_By^2-S_Cz^2\right)+\left(2\prod_{cyclic}\left(b^2-c^2\right)\right)xyz=0[/math]. [size=85]This is thhe barycentrlc equation of K028 which is isogonal transform os lemoine cubic[/size]