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K1258

b^2 c^2 (b^2 + c^2) x^2 (c^4 y - b^4 z) = 0

X(6), X(25), X(32), X(251), X(10547), X(17409), X(46765) → X(46771)

A'B'C' : cevian triangle of X(251)

see points below

Geometric properties :

K644 is the locus of pivots of pKs passing through the vertices of the Grebe triangle. The locus of isopivots is K177 and the locus of the poles is K1258 = pK(X32 x X251, X251). See also Table 57.

K1258 is the barycentric product X6 x K644 or X251 x K836.

K1258a

Points on K1258

Ω1176 = X(6) x X(251) = X(25) x X(1176), SEARCH = 0.145367739198673, on the lines {X6,X22},{X32,X206},{X83,X316},{X141,X1799}

***

Ω1342 = X(6) x X(1343)

= a^4 (a^2 + √(b^2c^2+c^2a^2+a^2b^2) : : , SEARCH = 0.175189582224064

Ω1343 = X(6) x X(1342)

= a^4 (a^2 - √(b^2c^2+c^2a^2+a^2b^2) : : , SEARCH = 14.5229482178684

These two latter points lie on the line X32,X184

***

Ω40404 = X(3162) x X(40404), SEARCH = 0.258510867770382, on the line {X32,X66}