X3331

INTERSECTION OF LINES X4X_6 AND X187X_237

X3331 = crossdifference of every pair of points on the line X2X520
< 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) { 4, 6 }: Van Aubel Line { 187, 237 }: Central Line L(187, 237) { 30, 1625 }: Central Line L(30, 1625) { 74, 1987 }: Central Line L(74, 1987) { 112, 1971 }: Central Line L(112, 1971) { 111, 2713 }: Central Line L(111, 2713) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1625 = TCC-PERSPECTOR OF X(163) (0.3499, 0.5717) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_1987 = 1st LEMOINE ANTIPARALLELS POINT (0.7533, -0.6902) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_1971 = CROSSDIFFERENCE OF PU(38) (1.3141, 4.2335) X_111 = PARRY POINT (0.9885, -0.0457) X_2713 = SR(X(99), X(107)) (0.9135, 0.4011) X_3331 = INTERSECTION OF LINES X(4)X(6) AND X(187)X(237) (0.7217, 1.5446) A B C X4 X6 X187 X237 X30 X1625 X74 X1987 X112 X1971 X111 X2713 X3331 (a, b, c) = (5, 6, 7) | AB = 1

X3331 (INTERSECTION OF LINES X4X_6 AND X187X_237) 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 \(f(A,B,C) = (\csc B \cos C)(\sin 2A - \sin 2B) - (\csc C \cos B)(\sin 2C - \sin 2A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.480212214527\)
▸ Incident Central Lines6 lines

{4, 6}, {30, 1625}, {74, 1987}, {111, 2713}, {112, 1971}, {187, 237}

▸ Functional Relations2 relations