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K1261

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X(2), X(3), X(376), X(1670), X(1671), X(7757), X(33706), X(46948)

infinite points of K003

vertices of the Thomson triangle Q1Q2Q3

other points below

Geometric properties :

K1261 is K080 for the Thomson triangle. Recall that K080 is spK(X3, X550) in ABC.

K1261 is a central stelloid with center O, point of inflexion on the curve. Its asymptotes are parallel at O to those of K003, in other words the altitudes of the circumnormal triangle N1N2N3.

K1261 is the isogonal transform of K1114 with respect to the Thomson triangle.

K1261 is a member of the pencil generated by K758 and the decomposed cubic which is the union of the Euler line and the circumcircle. This pencil also contains K764, K1260.

K1261 is also a member of the pencil of central stelloids generated by K080 and K100 which contains the decomposed cubic which is the union of the Brocard axis and the line at infinity counted twice. All these stelloids have the same asymptotes and pass through X(3), X(1670), X(1671).

Points on K1261 :

• vertices Q1, Q2, Q3 of the Thomson triangle.

• reflections R1, R2, R3 of Q1, Q2, Q3 in O.

• foci of (C), conic with center the midpoint X(8703) of X(3), X(376), inscribed in Q1Q2Q3. F1 and F2 are the real foci.