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An inconic with parameters x:y:z=a(b-c):b(c-a):c(a-b), (1) giving equation (2) (Kimberling 1998, pp. 238-239). Its focus is Kimberling center X_(101) and its conic section ...

Let points A^', B^', and C^' be marked off some fixed distance x along each of the sides BC, CA, and AB. Then the lines AA^', BB^', and CC^' concur in a point U known as the ...

The Yiu A-circle of a reference triangle DeltaABC is the circle passing through vertex A and the reflections of vertices B and C with respect to the opposite sides. The Yiu ...

The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles. It is the complement of ...

The de Longchamps ellipse of a triangle DeltaABC is the conic circumscribed on the incentral triangle and the Cevian triangle of the isogonal mittenpunkt X_(57). (Since a ...

The de Longchamps line is central line L_(32) with trilinear equation a^3alpha+b^3beta+c^3gamma=0 (Droussent 1953; Kimberling 1998, p. 150) which is the anticomplement of the ...

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...

The curve a hanging flexible wire or chain assumes when supported at its ends and acted upon by a uniform gravitational force. The word catenary is derived from the Latin ...

The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the ...