X1453

X452-BETH CONJUGATE OF X452

< 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, 6 }: Incenter–Symmedian Line { 28, 34 }: Central Line L(28, 34) { 31, 40 }: Central Line L(31, 40) { 4, 204 }: Central Line L(4, 204) { 56, 223 }: Central Line L(56, 223) { 212, 595 }: Central Line L(212, 595) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_452 = -HIRST INVERSE OF X(449) (0.5268, 0.1722) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_40 = BEVAN POINT (0.4286, -0.0292) X_4 = ORTHOCENTER (0.6122, 0.3958) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_223 = -CEVA CONJUGATE OF X(57) (0.4996, -0.0528) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_1453 = -BETH CONJUGATE OF X(452) (0.6101, 0.2792) A B C X452 X1 X6 X28 X34 X31 X40 X4 X204 X56 X223 X212 X595 X1453 (a, b, c) = (5, 6, 7) | AB = 1

X1453 (X452-BETH CONJUGATE OF X452) 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 \(f(a,b,c) = 3a^{3} + b^{3} + c^{3} + 3a^{2}b + 3a^{2}c + ab^{2} + ac^{2} - b^{2}c - bc^{2} + 2abc\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.823645052715\)
▸ Incident Central Lines13 lines

{1, 6}, {4, 204}, {28, 34}, {31, 40}, {43, 1009}, {56, 223}, {73, 995}, {84, 1039}, {212, 595}, {222, 1467}, {387, 950}, {581, 1193}, {614, 1468}