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X(3), X(6), X(23), X(25), X(111), X(187), X(1177), X(2393), X(2930) E = a^2 / (b^4 + c^4 - a^4 - b^2c^2) : : , X(32)-isoconjugate of X(23) point at infinity : isogonal of isotomic conjugate of X(858) isogonal conjugate of X(316) isogonal conjugates of the anticomplements of X(67), X(111) vertices of the tangential triangle |
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K108 is the only circular pK with pole X(32). Its pivot is X(23), the far-out point.
The real asymptote is parallel to the line X(6)X(25). Let A'B'C' be the tangential triangle i.e. the anticevian triangle of K. The three circles PAA', PBB', PCC' are concurrent if and only if P lies on K108 (together with the line at infinity). See also K008, property 4. |
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