X3475

INTERSECTION OF LINES X1X_4 AND X7X_55

X3475 = isogonal conjugate of X3477
< 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, 4 }: Incenter–Orthocenter Line { 7, 55 }: Central Line L(7, 55) { 2, 210 }: Central Line L(2, 210) { 142, 200 }: Central Line L(142, 200) { 165, 553 }: Central Line L(165, 553) { 12, 938 }: Central Line L(12, 938) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3477 = ISOGONAL CONJUGATE OF X(3475) (0.5688, 0.2234) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_2 = CENTROID (0.5374, 0.2000) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_200 = -CEVA CONJUGATE OF X(9) (0.4392, 0.1037) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_553 = POINT MAIA II (0.5963, 0.2857) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_3475 = INTERSECTION OF LINES X(1)X(4) AND X(7)X(55) (0.5740, 0.2434) A B C X3477 X1 X4 X7 X55 X2 X210 X142 X200 X165 X553 X12 X938 X3475 (a, b, c) = (5, 6, 7) | AB = 1

X3475 (INTERSECTION OF LINES X1X_4 AND X7X_55) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(2 + \cos A + \cos B + \cos C + \cos B \cos C : :\)
Search Value (6, 9, 13): \(1.439091871081\)
▸ Alternate Coordinates1 form

  • Trilinears: \(r + 3R + R \cos B \cos C : :\)

▸ Incident Central Lines9 lines

{1, 4}, {2, 210}, {7, 55}, {12, 938}, {142, 200}, {165, 553}, {329, 1001}, {942, 1788}, {954, 1617}

▸ Functional Relations2 relations