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X(3), X(194), X(12251)

infinite points of K410

A', B', C' : vertices of the ITB triangle, also on K410

A", B", C" : reflections of A', B', C' about O

Geometric properties :

The ITB triangle A'B'C' is defined at K1098.

K1102 meets K410 at three points on the line at infinity, three points A', B', C' on (O) and X(194) counting for three with the same tangent (passing through X6) and the same polar conic (the Wallace diagonal rectangular hyperbola which is the polar conic of X(20) in K004). The Kiepert hyperbola (H) of the ITB triangle also passes through X(194) with the same tangent and the points A', B', C', X(99), X(3413), X(3414).

The polar conic of X(12251) in K1102 is the rectangular hyperbola passing through X(4), X(20), X(376), X(1670), X(1671), X(3413), X(3414). It is the Wallace diagonal rectangular hyperbola of the ITB triangle hence it also contains its in/excenters. These points are obviously on K1098 and also K1100.

K1102 meets K004 at O counting for three with the same tangent (the Brocard axis) and six points on the circle (C) with center O, radius R √(1 + 8 sin2ω).