X3467

ISOGONAL CONJUGATE OF X3336

X3467 is the isogonal conjugate of X3336.
< 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) { 5, 79 }: Central Line L(5, 79) { 1, 195 }: Central Line L(1, 195) { 7, 499 }: Central Line L(7, 499) { 62, 1251 }: Central Line L(62, 1251) { 4, 3460 }: Central Line L(4, 3460) { 2120, 3469 }: Central Line L(2120, 3469) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3336 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(498) (0.6341, 0.3483) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_1 = INCENTER (0.5714, 0.2333) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_7 = GERGONNE POINT (0.5903, 0.2769) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_62 = ISOGONAL CONJUGATE OF X(18) (0.6446, 0.3409) X_1251 = ISOGONAL CONJUGATE OF X(1082) (0.5908, 0.2784) X_4 = ORTHOCENTER (0.6122, 0.3958) X_3460 = -CEVA CONJUGATE OF X(1) (0.5384, 0.2645) X_2120 = EIGENTRANSFORM OF X(5) (0.5135, 0.2811) X_3469 = ISOGONAL CONJUGATE OF X(3468) (0.6104, 0.5687) X_3467 = ISOGONAL CONJUGATE OF X(3336) (0.4625, 0.1294) A B C X3336 X5 X79 X1 X195 X7 X499 X62 X1251 X4 X3460 X2120 X3469 X3467 (a, b, c) = (5, 6, 7) | AB = 1

X3467 (ISOGONAL CONJUGATE OF X3336) 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 \(f(a,b,c) = 1/x(3336)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-43.975621058262\)

X3467 lies on the Napoleon cubic.

▸ Incident Central Lines7 lines

{1, 195}, {4, 3460}, {5, 79}, {7, 499}, {62, 1251}, {2120, 3469}, {3468, 3470}

▸ Functional Relations3 relations

Notes

Let J be the isogonal conjugate of the incenter I wrt the incentral triangle A'B'C', and let Ja, Jb, Jc be the reflections of J in B'C', C'A', A'B', resp. Then JaJbJc is perspective to ABC, and the perspector is X3467. See Antreas Hatzipolakis and César Lozada, euclid 3038.