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X(4), X(568), X(14254) infinite points of K003 points of (K) = pK(X6,X568) on (O) U', V', W' : projections of X(2) on the altitudes U = BC /\ X(568)U', V' and W' similarly more details and other points below |
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Geometric properties : |
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K1139 = spK(X3, X9730) is a stelloid with radial center X(5640) and asymptotes parallel to those of K003. See CL006 and CL055. Points on K1139 : • X(4), U', V', W' lie on the orthocentroidal circle. The two remaining common points M1, M2 lie on the perpendicular bisector of OH which passes through X(14254). • U, V, W lie on the sidelines of ABC and on the corresponding parallels at X(568) to the cevian lines of O. • foci of the inconic with center X(9730), the midpoint of O, X(568). • imaginary foci X(39641), X(39642) of the Brocard ellipse i.e. common points of the Brocard axis and the Kiepert hyperbola. These two points lie on K003 and (K). *** Consider a stelloidal psK(Ω, P, M) where Ω and P must lie on two circum-cubics K(Ω) and K(P) respectively. These two cubics are both K0s if and only if M lies on K1139. |
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