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X(2), X(3), X(6), X(3098), X(8667)

infinite points of K002

vertices of these triangles :

• Thomson (points Qi)

• tangential of Thomson (points Ri)

• CircumTangential (points Ti)

• Stammler = tangential of CircumTangential (points Si)

• X(2)-cevian of CircumTangential (points Mi)

other points below

Geometric properties :

(contributed by Peter Moses)

K1114 is the isogonal pK with pivot X(2) with respect to the CircumTangential triangle. The isopivot is X(3098) and the tertiary pivot P1 = X(33705) is the tangential of X(3098).

K1114 also contains the Thomson isogonal conjugates X(33707), X(33708) of X(1670), X(1671). Note that X(3098), X(33707), X(33708) are collinear. The Thomson isogonal transform of K1114 is K1261.

K1114 is a member of the pencil of cubics generated by the Thomson cubic K002 and the union of the line at infinity with the Thomson-Jerabek hyperbola. The central cubic K764 is another member. Any cubic of this pencil meets the line at infinity like the Thomson cubic K002. It meets the circumcircle at the vertices of the Thomson triangle and three other points – apart A, B, C – on an isogonal nK0 with root on the line GK. See K1115 which corresponds to K017 = nK0(X6, X385).

K172 and K1114 generate another pencil of cubics studied in Table 71.