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K1453

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X(2), X(3), X(6), X(30), X(265), X(1511), X(3163), X(3284), X(11064), X(14910), X(14919), X(51471), X(62569), X(62606), X(73090), X(73091), X(73092), X(73093)

vertices A', B', C' of the medial triangle with tangents passing through X(1511)

other points below

Geometric properties :

K1453 is the complement of K611 = pK(X2, X340).

The barycentric products of K1453 by X(4), X(16080), X(264) and X(1494) are K496, K1172, K1455 and K1456 respectively.

K1453 is the locus of point M such that the anticevian triangle of M is orthologic to the pedal triangle of X(186) or to the antipedal triangle of X(265). See CL048.

One of the orthology centers lies on the central cubic K1454 = pK(X3284, X12363), the other on a not very interesting cubic.

Points on K1453 :

• infinite points of the circum-conic (C) with perspector X(3), center X(6), passing through X(14919) on K1453.

• points S1, S2 on the Steiner inellipse (S) and on the trilinear polar (L) of X(69), passing through X{441, 525, 647, 905, 2504, 2510, 2519, 2522, 2523, 2524, 2525, 3265, etc} and also X(11064) on K1453.

Remark : these four points are real when ABC is obtus-angled.