X1405

X45-BETH CONJUGATE OF X45

X1405 = isogonal conjugate of X30608
< 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) { 31, 51 }: Central Line L(31, 51) { 44, 65 }: Central Line L(44, 65) { 57, 88 }: Central Line L(57, 88) { 35, 573 }: Central Line L(35, 573) { 169, 1046 }: Central Line L(169, 1046) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_1405 = -BETH CONJUGATE OF X(45) (0.6170, 0.3084) A B C X45 X6 X41 X31 X51 X44 X65 X57 X88 X35 X573 X169 X1046 X1405 (a, b, c) = (5, 6, 7) | AB = 1

X1405 (X45-BETH CONJUGATE OF X45) 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 \(u : v : w\) = X45
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.383876768896\)
▸ Incident Central Lines6 lines

{6, 41}, {31, 51}, {35, 573}, {44, 65}, {57, 88}, {169, 1046}

▸ Functional Relations1 relation

  • X1405 = isogonal conjugate of X30608