X1030

ISOGONAL CONJUGATE OF X1029

X1030 is the isogonal conjugate of X1029.
< 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, 6 }: Brocard Axis { 35, 37 }: Central Line L(35, 37) { 45, 198 }: Central Line L(45, 198) { 55, 199 }: Central Line L(55, 199) { 100, 594 }: Central Line L(100, 594) { 36, 1100 }: Central Line L(36, 1100) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1029 = CYCLOCEVIAN CONJUGATE OF X(1) (0.6026, 0.3320) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_199 = -CEVA CONJUGATE OF X(6) (0.4796, 0.0487) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_594 = ISOGONAL CONJUGATE OF X(593) (0.5025, 0.1672) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_1030 = ISOGONAL CONJUGATE OF X(1029) (0.5271, 0.1468) A B C X1029 X3 X6 X35 X37 X45 X198 X55 X199 X100 X594 X36 X1100 X1030 (a, b, c) = (5, 6, 7) | AB = 1

X1030 (ISOGONAL CONJUGATE OF X1029) 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 \(f(a,b,c) = a + 2(a + b + c) \cos A\)
Barycentrics: \(a^{2} (a^{3} + a^{2} (b + c) - a (b^{2} + b c + c^{2}) - (b + c) (b^{2} + c^{2})) : :\)
Search Value (6, 9, 13): \(4.208787799605\)
▸ Incident Central Lines6 lines

{3, 6}, {35, 37}, {36, 1100}, {45, 198}, {55, 199}, {100, 594}

▸ Functional Relations8 relations