X1045

X42-CEVA CONJUGATE OF X1

X1045 = X42-Ceva conjugate of X1
< 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) { 9, 43 }: Central Line L(9, 43) { 1, 75 }: Central Line L(1, 75) { 40, 511 }: Central Line L(40, 511) { 42, 894 }: Central Line L(42, 894) { 192, 869 }: Central Line L(192, 869) { 190, 872 }: Central Line L(190, 872) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1 = INCENTER (0.5714, 0.2333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_40 = BEVAN POINT (0.4286, -0.0292) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_1045 = -CEVA CONJUGATE OF X(1) (0.6065, 0.2647) A B C X42 X1 X9 X43 X75 X40 X511 X894 X192 X869 X190 X872 X1045 (a, b, c) = (5, 6, 7) | AB = 1

X1045 (X42-CEVA 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 \(f(a,b,c) = -u^{2} + v^{2} + w^{2} + vw + wu + uv\),\(u : v : w\) = X2
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.847264956880\)
▸ Incident Central Lines7 lines

{1, 75}, {6, 2665}, {9, 43}, {40, 511}, {42, 894}, {190, 872}, {192, 869}

▸ Functional Relations4 relations