X3065

ISOGONAL CONJUGATE OF X484

X3065 is the isogonal conjugate of X484.
< 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) { 11, 79 }: Central Line L(11, 79) { 30, 80 }: Central Line L(30, 80) { 8, 191 }: Central Line L(8, 191) { 21, 214 }: Central Line L(21, 214) { 1, 399 }: Central Line L(1, 399) { 9, 1030 }: Central Line L(9, 1030) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_8 = NAGEL POINT (0.4694, 0.1333) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_1 = INCENTER (0.5714, 0.2333) X_399 = PARRY REFLECTION POINT (0.0032, 0.9936) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1030 = ISOGONAL CONJUGATE OF X(1029) (0.5271, 0.1468) X_3065 = ISOGONAL CONJUGATE OF X(484) (0.8717, -0.1686) A B C X484 X11 X79 X30 X80 X8 X191 X21 X214 X1 X399 X9 X1030 X3065 (a, b, c) = (5, 6, 7) | AB = 1

X3065 (ISOGONAL CONJUGATE OF X484) 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 \(f(A,B,C) = 1/[1 + 2(\cos A - \cos B - \cos C)]\)
Barycentrics: \(af(A,B,C): bf(B,C,A) : cf(C,A,B)\)
Search Value (6, 9, 13): \(5.239355936512\)

X3065 lies on the Neuberg cubic.

▸ Incident Central Lines14 lines

{1, 399}, {4, 1768}, {8, 191}, {9, 1030}, {11, 79}, {21, 214}, {30, 80}, {202, 1251}, {314, 1227}, {758, 1320}, {1157, 3465}, {1389, 2800}, {2132, 3466}, {2346, 2801}

▸ Functional Relations7 relations