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K1449

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X(1), X(740), X(741), X(5018), X(5143), X(5524), X(7281), X(7312), X(8481), X(8482), X(61432), X(61433), X(61434), X(70222), X(72990), X(72991), X(72992)

A', B', C' traces of the trilinear polar of X(4369) passing through X(804), X(3023)

Geometric properties :

K1449 = cK(#X1, X4369) is the excentral-polar-circle-inverse of the Wallace diagonal rectangular hyperbola. It is a member of CL003 where more general properties are given.

It is a strophoid with singular focus X(741) and node X(1) with nodal tangents parallel to the asymptotes of the Kiepert hyperbola.

For every point M = u:v:w ≠ X(1), the point M' is a point of K1449 :

M' = a (a v - b u) (a w - c u) [(-a+b+c) (b-c) (b+c) u + (a-b) (a b + c^2) v + (c-a) (a c + b^2) w] : : .