E

X(72896) = X(1)X(6)∩X(105)X(517)

Barycentrics    a*(2*a^4-3*a^3*b+a^2*b^2-a*b^3+b^4-3*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+2*b^2*c^2-a*c^3-2*b*c^3+c^4) : :
X(72896) = X[1]+X[5526], 2*X[1083]-X[41391], X[840]-2*X[5126], 5*X[3616]-X[70627]

Antreas Hatzipolakis and Ercole Suppa, euclid 10098.

X(72896) lies on these lines: {1, 6}, {8, 27132}, {11, 3008}, {36, 67517}, {56, 14878}, {57, 35273}, {65, 52015}, {105, 517}, {109, 241}, {277, 5805}, {519, 40609}, {663, 905}, {748, 28125}, {840, 5126}, {902, 35293}, {971, 18461}, {1054, 9441}, {1155, 5144}, {1319, 1362}, {1323, 1456}, {1737, 62674}, {2340, 3722}, {2348, 2809}, {2646, 39789}, {3315, 62799}, {3616, 27187}, {3744, 41276}, {3915, 7084}, {4414, 37597}, {4845, 45272}, {4904, 28849}, {5308, 9347}, {5440, 8299}, {5584, 51622}, {5723, 69459}, {5886, 16020}, {5988, 11725}, {7677, 38459}, {8616, 54474}, {9502, 39251}, {10481, 60883}, {15524, 36056}, {15746, 50371}, {16688, 65416}, {21002, 53996}, {24774, 48900}, {24928, 67331}, {24929, 71703}, {28534, 34578}, {29571, 70915}, {30385, 39795}, {30386, 39794}, {34049, 43047}, {43037, 67726}, {43057, 53617}, {44669, 68623}, {47621, 64013}, {47623, 71544}, {65524, 69084}

X(72896) = midpoint of X(1) and X(5526)
X(72896) = reflection of X(i) in X(j) for these {i,j}: {840, 5126}, {41391, 1083}
X(72896) = reflection of X(i) in the line X(j)X(k) for these {i,j,k}: {105, 513, 1960}, {67382, 1538, 3309}
X(72896) = foot of the perpendicular from X(i) to the line X(j)X(k) for these {i,j,k}: {663, 1, 6}, {1, 663, 905}
X(72896) = perspector of the circumconic through X(100)and X(39273)
X(72896) = intersection, other than A, B, C, of the circumconics: {{A,B,C,X(9),X(2725)}, {A,B,C,X(105),X(43065)}, {A,B,C,X(106),X(60360)}, {A,B,C,X(2284),X(2742)}, {A,B,C,X(14074),X(52985)}}
X(72896) = inverse of X(5728) in incircle
X(72896) = inverse of X(18412) in Suppa-Cucoanes circle
X(72896) = Gibert-Burek-Moses concurrent circles image of X(5223)
X(72896) = X(21)-beth conjugate of X(43065)
X(72896) = X(i)-he conjugate of X(j) for these {i,j}: {57, 60846},{60666, 1743}
X(72896) = cross-difference of every pair of points on the line X(513)X(40131)
X(72896) = pole of the line {667, 22769} with respect to circumcircle
X(72896) = pole of the line {3309, 5728} with respect to incircle
X(72896) = pole of the line {3309, 18412} with respect to Suppa-Cucoanes circle
X(72896) = pole of the line {55, 2809} with respect to Feuerbach hyperbola
X(72896) = pole of the line {513, 2280} with respect to Hofstadter inellipse
X(72896) = pole of the line {100, 66514} with respect to Hutson-Moses hyperbola
X(72896) = pole of the line {650, 37597} with respect to Steiner inellipse
X(72896) = pole of tripolar of X(60581) with respect to orthoptic circle of Feuerbach hyperbola
X(72896) = pole of the line {142, 24685} with respect to dual conic of Yff parabola
X(72896) = {X(i),X(j)}-harmonic conjugate of X(k) for these (i,j,k): {1, 238, 43065}, {1, 5526, 518}, {1279, 6603, 1}

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X(72897) = X(265)X(6760)∩X(7728)X(13557)

Barycentrics    (a^2-b^2-c^2)*(a^8+a^6*b^2-4*a^4*b^4+a^2*b^6+b^8-3*a^6*c^2+a^4*b^2*c^2+a^2*b^4*c^2-3*b^6*c^2+3*a^4*c^4-a^2*b^2*c^4+3*b^4*c^4-a^2*c^6-b^2*c^6)*(a^8-3*a^6*b^2+3*a^4*b^4-a^2*b^6+a^6*c^2+a^4*b^2*c^2-a^2*b^4*c^2-b^6*c^2-4*a^4*c^4+a^2*b^2*c^4+3*b^4*c^4+a^2*c^6-3*b^2*c^6+c^8)*(a^10-2*a^8*b^2+a^6*b^4-a^4*b^6+2*a^2*b^8-b^10-2*a^8*c^2+5*a^6*b^2*c^2-a^4*b^4*c^2-5*a^2*b^6*c^2+3*b^8*c^2+a^6*c^4-a^4*b^2*c^4+6*a^2*b^4*c^4-2*b^6*c^4-a^4*c^6-5*a^2*b^2*c^6-2*b^4*c^6+2*a^2*c^8+3*b^2*c^8-c^10) : :

Antreas Hatzipolakis and Ercole Suppa, euclid 10098.

X(72897) lies on the circumconic {{A,B,C,X(265),X(50435)}} and these lines: {265, 6760}, {7728, 13557}

X(72897) = QAP4: Isogonal Center of X(12111)

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X(72898) = X(113)X(12095)∩X(125)X(12096)

Barycentrics    (a^2-b^2-c^2)^2*(2*a^24-7*a^22*b^2+a^20*b^4+28*a^18*b^6-54*a^16*b^8+56*a^14*b^10-56*a^12*b^12+54*a^10*b^14-28*a^8*b^16-a^6*b^18+7*a^4*b^20-2*a^2*b^22-7*a^22*c^2+38*a^20*b^2*c^2-56*a^18*b^4*c^2-17*a^16*b^6*c^2+82*a^14*b^8*c^2+20*a^12*b^10*c^2-132*a^10*b^12*c^2+66*a^8*b^14*c^2+37*a^6*b^16*c^2-42*a^4*b^18*c^2+12*a^2*b^20*c^2-b^22*c^2+a^20*c^4-56*a^18*b^2*c^4+178*a^16*b^4*c^4-142*a^14*b^6*c^4-132*a^12*b^8*c^4+224*a^10*b^10*c^4+16*a^8*b^12*c^4-158*a^6*b^14*c^4+87*a^4*b^16*c^4-28*a^2*b^18*c^4+10*b^20*c^4+28*a^18*c^6-17*a^16*b^2*c^6-142*a^14*b^4*c^6+336*a^12*b^6*c^6-146*a^10*b^8*c^6-274*a^8*b^10*c^6+262*a^6*b^12*c^6-32*a^4*b^14*c^6+30*a^2*b^16*c^6-45*b^18*c^6-54*a^16*c^8+82*a^14*b^2*c^8-132*a^12*b^4*c^8-146*a^10*b^6*c^8+440*a^8*b^8*c^8-140*a^6*b^10*c^8-158*a^4*b^12*c^8-12*a^2*b^14*c^8+120*b^16*c^8+56*a^14*c^10+20*a^12*b^2*c^10+224*a^10*b^4*c^10-274*a^8*b^6*c^10-140*a^6*b^8*c^10+276*a^4*b^10*c^10-210*b^14*c^10-56*a^12*c^12-132*a^10*b^2*c^12+16*a^8*b^4*c^12+262*a^6*b^6*c^12-158*a^4*b^8*c^12+252*b^12*c^12+54*a^10*c^14+66*a^8*b^2*c^14-158*a^6*b^4*c^14-32*a^4*b^6*c^14-12*a^2*b^8*c^14-210*b^10*c^14-28*a^8*c^16+37*a^6*b^2*c^16+87*a^4*b^4*c^16+30*a^2*b^6*c^16+120*b^8*c^16-a^6*c^18-42*a^4*b^2*c^18-28*a^2*b^4*c^18-45*b^6*c^18+7*a^4*c^20+12*a^2*b^2*c^20+10*b^4*c^20-2*a^2*c^22-b^2*c^22) : :

Antreas Hatzipolakis and Ercole Suppa, euclid 10098.

X(72898) lies on these lines: {113, 12095}, {125, 12096}

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