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X(11), X(55), X(497), X(650), X(11934) A'B'C' : cevian triangle of X(497) QaQbQc : anticevian triangle of X(650) PaPbPc : Mandart incircle triangle Pa', Pb', Pc' : isoconjugates of Pa, Pb, Pc |
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Geometric properties : |
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K925 is the pK with pivot X(497) invariant under the isoconjugation with fixed point X(650). Its pole Ω and isopivot Q are Ω = X(650)^2 = X(14936) and Q = Ω ÷ X(497) = X(14935) The incircle and the Mandart inellipse meet at X(11) and three other points which are the vertices of the Mandart incircle triangle. K925 passes through the vertices of this latter triangle and several other related triangles listed above. Note that any two of these triangles (including ABC) are perspective with perspector on the cubic. In other words, K925 is a pK with respect to any of the five mentioned triangles (and actually wrt infinitely many others). For example : • K925 is the pK with pivot X(11), isopivot X(650) wrt PaPbPc. • K925 is the pK with pivot X(650), isopivot X(497) wrt QaQbQc. See the related K554 where a generalization is given and also K927. |