McCay-Griffiths Cubic

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Given a triangle and a point , the pedal triangle of is formed by the feet of the perpendiculars from to the sides . The circumcircle of the pedal triangle is called the pedal circle of (shown in black).


The McCay–Griffiths cubic of is the set of all points such that the pedal circle of is tangent to the nine-point circle (shown in green) of . Its pivot point is the circumcenter (Kimberling center ).

Let , , be the side lengths; , , the parameters of in Conway triangle notation and , , the excenters of .

Then the equation of the McCay–Griffiths cubic of in barycentric coordinates is


where the sum is cyclic over all six permutations of , , .

The McCay–Griffiths cubic passes through the points , , and the Kimberling centers , , , , , , [1].

You can drag the vertices , , and the point .


Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA




[1] Encyclopedia of Triangle Centers (ETC).

[2] B. Gilbert. "K003 McCay Cubic=Griffiths Cubic." (Jul 29, 2022)

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