too complicated to be written here. Click on the link to download a text file. X(3), X(25), X(64), X(159), X(17809), X(33524) vertices of the tangential triangle of the Thomson triangle other points below Geometric properties :
 K172 = pK(X32, X3) is a pK passing through the vertices Q1, Q2, Q3 of the Thomson triangle and also the vertices R1, R2, R3 of the tangential triangle of the Thomson triangle. See Table 27, paragraph Lemoine point of T(P), and also K1110, K1111, K1112. More generally, any pK passing through the vertices of the tangential triangle of the Thomson triangle must have its pivot on K1109. The pole and isopivot lie on two not very interesting circumcubics. K1109 meets the line at infinity at the same points as pK(X6, P∞) where P∞ lies on the lines {2,389}, {22,1498}, {66,69}, etc, SEARCH = -1.42577077381013. K1109 meets the circumcircle again at the same points as pK(X6, Po) where Po lies on the lines {2,1350}, {20,343}, {22,69}, {51,631}, etc, SEARCH = 54.3351372729986. Po and P∞ are X(33522) and X(33523) in ETC.