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X(3), X(15), X(16), X(194), X(25424), X(32465), X(32466), X(32515), X(32595), X(32596), X(32597)

A', B', C' : vertices of the ITB triangle

Jo, Ja, Jb, Jc : in/excenters of the ITB triangle

Geometric properties :

The ITB triangle A'B'C' is defined at K1098 and 𝞱 denotes the isogonal conjugation with respect to this triangle.

K1105 is the locus of M such that the line M𝞱(M) is parallel to the line X(3)X(194), the Euler line of the ITB triangle.

K001 and K1105 meet at X(3), X(15), X(16), the circular points at infinity and four other points on a same circle (C) with center X(182), the center of the Brocard and 1st Lemoine circles.

The singular focus F of K1105 is X(110) of the ITB triangle. It is the reflection in X(3) of X(24524) = X(74) of the ITB triangle. F lies on the lines {32, 26714}, {99, 182}, {110, 11328}, {691, 32442}, {805, 2080}, {1350, 30254}, {1351, 32514}, {1976, 6037}.

Other points on K1105 :

X(32595) = X(399) of the ITB triangle on the lines {3,25424},{6,1569} and on the Stammler circle.

X(32596) = X(616) of the ITB triangle on the lines {4, 3104}, {16, 7709}, {98, 3098}, {511, 3180}, {616, 2782}, {3094, 16941}, {5980, 18906}, {9821, 22532}, {11257, 22531}, {12251, 14540}, {16940, 22707}, {31683, 31701} and on (H).

X(32597) = X(617) of the ITB triangle on the lines {4, 3105}, {15, 7709}, {98, 3098}, {511, 3181}, {617, 2782}, {3094, 16940}, {5981, 18906}, {9821, 22531}, {11257, 22532}, {12251, 14541}, {16941, 22708}, {31684, 31702} and on (H).