X602

INTERSECTION OF LINES X3X_31 AND X56X_255

< 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) { 3, 31 }: Central Line L(3, 31) { 36, 47 }: Central Line L(36, 47) { 1, 201 }: Central Line L(1, 201) { 4, 238 }: Central Line L(4, 238) { 56, 255 }: Central Line L(56, 255) { 40, 595 }: Central Line L(40, 595) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_1 = INCENTER (0.5714, 0.2333) X_201 = -CEVA CONJUGATE OF X(12) (0.4897, 0.1062) X_4 = ORTHOCENTER (0.6122, 0.3958) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_255 = ISOGONAL CONJUGATE OF X(158) (0.4217, 0.0365) X_40 = BEVAN POINT (0.4286, -0.0292) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_602 = INTERSECTION OF LINES X(3)X(31) AND X(56)X(255) (0.8182, 0.6170) A B C X3 X31 X36 X47 X1 X201 X4 X238 X56 X255 X40 X595 X602 (a, b, c) = (5, 6, 7) | AB = 1

X602 (INTERSECTION OF LINES X3X_31 AND X56X_255) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(\sin^{2} A - \cos A : \sin^{2} B - \cos B : \sin^{2} C - \cos C\)
Barycentrics: \((\sin A)(\sin^{2} A - \cos A) : (\sin B)(\sin^{2} B - \cos B) : (\sin C)(\sin^{2} C - \cos C)\)
Search Value (6, 9, 13): \(-4.498622857261\)
▸ Incident Central Lines13 lines

{1, 201}, {3, 31}, {4, 238}, {5, 748}, {36, 47}, {40, 595}, {56, 255}, {140, 750}, {171, 631}, {371, 605}, {372, 606}, {517, 582}, {774, 1062}