X1018

X512-CROSS CONJUGATE OF X1

X1018 = isogonal conjugate of X1019
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 1, 39 }: Central Line L(1, 39) { 9, 80 }: Central Line L(9, 80) { 100, 101 }: Central Line L(100, 101) { 63, 544 }: Central Line L(63, 544) { 40, 728 }: Central Line L(40, 728) { 163, 643 }: Central Line L(163, 643) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1 = INCENTER (0.5714, 0.2333) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_9 = MITTENPUNKT (0.5110, 0.1615) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_544 = DIRECTION OF VECTOR AX + BX + CX, where X = X(101) (0.1236, 0.6161) X_40 = BEVAN POINT (0.4286, -0.0292) X_728 = INTERSECTION OF LINES X(8)X(9) AND X(57)X(345) (0.3648, 0.0624) X_163 = TRILINEAR PRODUCT X(6)*X(110) (0.3174, 0.5883) X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA (0.0142, 0.3704) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) A B C X512 X1 X39 X9 X80 X100 X101 X63 X544 X40 X728 X163 X643 X1018 (a, b, c) = (5, 6, 7) | AB = 1

X1018 (X512-CROSS CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = (b + c)/(b - c)\)
Search Value (6, 9, 13): \(3.538160336300\)
▸ Incident Central Lines11 lines

{1, 39}, {9, 80}, {40, 728}, {63, 544}, {99, 813}, {100, 101}, {163, 643}, {190, 646}, {346, 573}, {519, 672}, {664, 1025}

▸ Functional Relations7 relations

Notes

X1018 is the intersection, other than the vertices of the Gemini 18 triangle, of the {ABC, Gemini 18}-circumconic and {Gemini 17, Gemini 18}-circumconic. (Randy Hutson, November 30, 2018)