X603

X58-CEVA CONJUGATE OF X56

X603 = isogonal conjugate of X318
< 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) { 28, 34 }: Central Line L(28, 34) { 3, 73 }: Central Line L(3, 73) { 36, 47 }: Central Line L(36, 47) { 31, 56 }: Central Line L(31, 56) { 1, 104 }: Central Line L(1, 104) { 33, 84 }: Central Line L(33, 84) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1 = INCENTER (0.5714, 0.2333) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_603 = -CEVA CONJUGATE OF X(56) (0.5992, 0.1851) A B C X58 X56 X28 X34 X3 X73 X36 X47 X31 X1 X104 X33 X84 X603 (a, b, c) = (5, 6, 7) | AB = 1

X603 (X58-CEVA CONJUGATE OF X56) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\cos^{2} A - \cos A : :\)
Barycentrics: \((\sin A)(\cos^{2} A - \cos A) : (\cos B)(\cos^{2} B - \cos B) : (\cos C)(\cos^{2} C - \cos C)\)
Search Value (6, 9, 13): \(-0.504249278091\)
▸ Alternate Coordinates3 forms

  • Trilinears: \((\cos A) (1 - \cos A) : :\)

  • Trilinears: \((\cos A) \sin^{2}(A/2) : :\)

  • Trilinears: \(a^{2} (b^{2} + c^{2} - a^{2})/(b + c - a) : :\)

▸ Incident Central Lines15 lines

{1, 104}, {3, 73}, {6, 1035}, {12, 750}, {28, 34}, {31, 56}, {33, 84}, {36, 47}, {41, 911}, {48, 577}, {63, 201}, {77, 283}, {171, 388}, {223, 580}, {404, 651}

▸ Functional Relations8 relations