X1450

X392-BETH CONJUGATE OF X392

< 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) { 6, 41 }: Central Line L(6, 41) { 65, 244 }: Central Line L(65, 244) { 1, 631 }: Central Line L(1, 631) { 57, 957 }: Central Line L(57, 957) { 3, 1057 }: Central Line L(3, 1057) { 36, 1064 }: Central Line L(36, 1064) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_392 = X(1,6)∩X(10,11) (0.5265, 0.1800) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_1 = INCENTER (0.5714, 0.2333) X_631 = 3/5*OG (0.5224, 0.1608) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_957 = ISOGONAL CONJUGATE OF X(956) (0.6245, 0.3599) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1057 = ISOGONAL CONJUGATE OF X(1056) (0.5671, 0.2170) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1064 = INTERSECTION OF LINES X(1)X(4) AND X(3)X(31) (0.5648, 0.2070) X_1450 = -BETH CONJUGATE OF X(392) (0.6088, 0.2886) A B C X392 X6 X41 X65 X244 X1 X631 X57 X957 X3 X1057 X36 X1064 X1450 (a, b, c) = (5, 6, 7) | AB = 1

X1450 (X392-BETH CONJUGATE OF X392) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X392
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.579715934304\)
▸ Incident Central Lines11 lines

{1, 631}, {3, 1057}, {6, 41}, {31, 1470}, {36, 1064}, {42, 1319}, {57, 957}, {65, 244}, {386, 1420}, {388, 978}, {1191, 1466}