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- W2556347255 abstract "The Thomson cubic meets the circumcircle at A, B, C and three other points Q1, Q2, Q3 which are the vertices of the Thomson triangle T . We investigate some properties of this triangle and, in particular, its connexion with the equiareality center X5373 related with the Steinhaus’ problem. 1 Definition and properties of the Thomson triangle 1.1 Definition of T Let K002 be the Thomson cubic i.e. the isogonal pivotal cubic with pivot the centroid G of the reference triangle ABC. It is the locus of point M such that G, M and its isogonal conjugate M ∗ are collinear. This cubic has numerous properties which we will not consider here. See [2] for further details. K002 meets the circumcircle (O) of ABC again at three (always real) points Q1, Q2, Q3 which are the vertices of a triangle T we shall call the Thomson triangle. Most of the results in this paper were obtained through manipulations of symmetric functions of the roots of third degree polynomials. In particular, the (barycentric) equation of the cubic that is the union of the sidelines of T is X cyclic � a 4 yz( x + 2y + 2z) 2b 2 c 2 x(x y)(x z) � = 2 X cyclic b 2 c 2 x ! X" @default.
- W2556347255 created "2016-11-30" @default.
- W2556347255 creator A5044998755 @default.
- W2556347255 date "2016-01-01" @default.
- W2556347255 modified "2023-09-27" @default.
- W2556347255 title "On the Thomson Triangle" @default.
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