X3332

INTERSECTION OF LINES X1X_7 AND X4X_6

X3332 = crossdifference of every pair of points on the line X520X657
< 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) { 1, 7 }: Soddy Line { 4, 6 }: Van Aubel Line { 278, 1456 }: Central Line L(278, 1456) { 2, 1754 }: Central Line L(2, 1754) { 219, 2550 }: Central Line L(219, 2550) { 42, 2947 }: Central Line L(42, 2947) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_1456 = -BETH CONJUGATE OF X(516) (0.7238, 1.0576) X_2 = CENTROID (0.5374, 0.2000) X_1754 = MIMOSA TRANSFORM OF X(284) (0.6792, 0.4313) X_219 = -CEVA CONJUGATE OF X(55) (0.4277, 0.0625) X_2550 = INSIMILICENTER(SPIEKER CIRCLE, (X(4),2R)) (0.5298, 0.2051) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_2947 = EXCENTRAL-ISOGONAL CONJUGATE OF X(19) (0.4145, -0.3913) X_3332 = INTERSECTION OF LINES X(1)X(7) AND X(4)X(6) (0.6039, 0.3085) A B C X1 X7 X4 X6 X278 X1456 X2 X1754 X219 X2550 X42 X2947 X3332 (a, b, c) = (5, 6, 7) | AB = 1

X3332 (INTERSECTION OF LINES X1X_7 AND X4X_6) 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 \(f(A,B,C) = (\cos C)(1 + \cos B)(\cos C - \cos A)(\sin 2A - \sin 2B) - (\cos B)(1 + \cos C)(\cos A - \cos B)(\sin 2C - \sin 2A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-0.810586295840\)
▸ Incident Central Lines6 lines

{1, 7}, {2, 1754}, {4, 6}, {42, 2947}, {219, 2550}, {278, 1456}

▸ Functional Relations1 relation

  • X3332 = crossdifference of every pair of points on the line X520X657