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X(1), X(2), X(3), X(4), X(6), X(81), X(284), X(1172), X(1751), X(1780), X(37543), X(40572)

X(45126) → X(45130)

see points below

Geometric properties :

K1242 is a member of Table 30.

It is invariant under the Cundy-Parry like transformation f, mentioned in Table 30, that maps M onto the intersection of the lines GM and KM*, where M* is the isogonal conjugate of M. See further details in CL061.

Centers on the curve

Q1 = a (a+b-c) (a-b+c) (a^3+a^2 b-a b^2-b^3+a^2 c-2 a b c-b^2 c-a c^2-b c^2-c^3) : : , SEARCH = 3.20603511744052, on the lines {X1,X4}, {X2,X914}, {X6,X1214}, {X48,X1763}, {X57,X77}, {X63,X1993}

Q2 = a (a^3-a b^2-2 a b c-b^2 c-a c^2-b c^2) (a^2 b-b^3+2 a^2 c+2 a b c+2 a c^2+b c^2) (2 a^2 b+2 a b^2+a^2 c+2 a b c+b^2 c-c^3) : : , SEARCH = 1.66290839885526, on the lines {X1,X1751}, {X3,X81}, {X6,X943}

Q3 = a^2 (a^2-b^2-c^2) (a^4-2 a^2 b^2+b^4-2 a^2 b c-2 a b^2 c-2 a b c^2-c^4) (a^4-b^4-2 a^2 b c-2 a b^2 c-2 a^2 c^2-2 a b c^2+c^4) : : , SEARCH = 4.04329056757842 , on the lines {X2,X1172}, {X3,X1779}, {X6,X1214}, {X48,X3173}

Q4 = a^2 (a^3-a^2 b-a b^2+b^3-a^2 c-4 a b c-b^2 c-3 a c^2-3 b c^2-c^3) (a^3-a^2 b-3 a b^2-b^3-a^2 c-4 a b c-3 b^2 c-a c^2-b c^2+c^3) : : , SEARCH = 1.63619355373526, on the lines {X6,X1780}, {X25,X584}, {X37,X2271}, {X42,X2911}

Q5 = a (a^3-a^2 b-a b^2+b^3+a^2 c+b^2 c-a c^2-b c^2-c^3) (a^3+a^2 b-a b^2-b^3-a^2 c-b^2 c-a c^2+b c^2+c^3) (a^4-b^4+2 a^2 b c+2 a b^2 c+2 a b c^2+2 b^2 c^2-c^4) : : , SEARCH = 4.05334380325741, on the lines {X2,X914}, {X3,X2164}, {X6,X1069}, {X90,X1172}

Q6 = a (a^3+a^2 b+a b^2+b^3-a^2 c-2 a b c-b^2 c-a c^2-b c^2+c^3) (a^3-a^2 b-a b^2+b^3+a^2 c-2 a b c-b^2 c+a c^2-b c^2+c^3) (a^4-a^3 b-a^2 b^2+a b^3-a^3 c-2 a^2 b c+3 a b^2 c+2 b^3 c-a^2 c^2+3 a b c^2+4 b^2 c^2+a c^3+2 b c^3) : : , SEARCH = -0.865277472231444, on the lines {X3,X2164}, {X4,X2911}