Τρίτη, 10 Δεκεμβρίου 2019

NEW POINTS

X(38808) =  ISOGONAL CONJUGATE OF X(8798)

Barycentrics    (a^2+b^2-c^2) (a^2-b^2+c^2) (a^4-2 a^2 b^2+b^4-a^2 c^2-b^2 c^2) (3 a^4-2 a^2 b^2-b^4-2 a^2 c^2+2 b^2 c^2-c^4) (a^4-a^2 b^2-2 a^2 c^2-b^2 c^2+c^4) : :
Barycentrics    SB SC (S^2+SA SC) (-S^2+2 SB SC) (-2 S^2+(SA+SB) SC) : :
X(38808) = X(4)-3*X(3462),X(4)-6*X(33549),8*X(140)-3*X(15319)

See Kadir Altintas and Ercole Suppa, Euclid 904 .

X(38808) lies on the cubics K361, K618 and these lines: {3,14371}, {4,54}, {95,253}, {96,10018}, {97,3346}, {107,10282}, {140,6760}, {154,14249}, {185,19209}, {186,18349}, {550,933}, {648,7488}, {1075,11202}, {1093,9707}, {1141,33640}, {1249,33629}, {1656,19176}, {1990,14533}, {2052,19357}, {2167,5882}, {2190,3668}, {2883,10152}, {3515,9307}, {3516,16030}, {3517,19173}, {4993,5068}, {5056,19188}, {5059,16251}, {6146,14165}, {7691,35311}, {7768,18831}, {8794,37070}, {8795,14528}, {10990,19208}, {14615,35602}, {14863,15712}, {16252,34170}, {19185,32534}, {19192,35477}, {19193,30714}

X(38808) = isogonal conjugate of X(8798)
X(38808) = reflection of X(3462) in X(33549)
X(38808) = polar conjugate of X(13157)
X(38808) = X(95)-Ceva conjugate of X(275)
X(38808) = X(154)-cross conjugate of X(33629)
X(38808) = X(i)-isoconjugate of X(j) for these (i,j): (5,19614), (48,13157), (51,19611), (216,2184), (343,2155)
X(38808)= X(i)-reciprocal conjugate of X(j) for these {i,j}: {6,8798}, {20,343}, {54,1073}, {95,34403}, {97,15394}
X(38808) = X(4)-vertex conjugate of X(14371)
X(38808) = cevapoint of X(154) and X(1249)
X(38808) = barycentric product X(i)*X(j) for these (i,j): (20,275), (54,15466), (95,1249), (97,14249), (154,276)
X(38808) = barycentric quotient X(i)/X(j) for these {i,j}: {20,343}, {54,1073}, {95,34403}, {97,15394}, {154,216}
X(38808) = trilinear product X(i)*X(j) for these (i,j): (20,2190), (54,1895), (92,33629), (95,204), (275,610)
X(38808) = trilinear quotient X(i)/X(j) for these (i,j): (54,19614), (95,19611), (204,51), (275,2184), (610,216)
X(38808) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): (54,8884,275), (275,8884,19169)



 

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