X3317

ISOGONAL CONJUGATE OF X3312

X3317 is the isogonal conjugate of X3312.
< 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) { 4, 615 }: Central Line L(4, 615) { 486, 631 }: Central Line L(486, 631) { 3, 1132 }: Central Line L(3, 1132) { 5, 1131 }: Central Line L(5, 1131) { 226, 1373 }: Central Line L(226, 1373) { 376, 1328 }: Central Line L(376, 1328) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1588 = POINT CASTOR II (0.5955, 0.2203) X_4 = ORTHOCENTER (0.6122, 0.3958) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_631 = 3/5*OG (0.5224, 0.1608) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1132 = ARCTAN(-2) KIEPERT POINT (0.8864, -0.3774) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_1131 = ARCTAN(2) KIEPERT POINT (0.5904, 0.2888) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_1373 = 1st GRIFFITHS POINT (0.5861, 0.2673) X_376 = CENTROID OF THE ANTIPEDAL TRIANGLE OF X(2) (0.4626, 0.0042) X_1328 = ARCTAN(-3) KIEPERT POINT (0.4997, 1.5024) X_3317 = ISOGONAL CONJUGATE OF X(3312) (0.4661, 0.1442) A B C X1588 X4 X615 X486 X631 X3 X1132 X5 X1131 X226 X1373 X376 X1328 X3317 (a, b, c) = (5, 6, 7) | AB = 1

X3317 (ISOGONAL CONJUGATE OF X3312) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/(\cos A - 2 \sin A) : 1/(\cos B - 2 \sin B) : 1/(\cos C - 2 \sin C)\)
Barycentrics: \((\sin A)/(\cos A - 2 \sin A) : (\sin B)/(\cos B - 2 \sin B) : (\sin C) /(\cos C - 2 \sin C)\)
Search Value (6, 9, 13): \(15.176522771038\)
▸ Alternate Coordinates1 form

  • Trilinears: \(\sec(A + t) : \sec(B + t) : \sec(C + t)\), where t = arctan(2)

▸ Incident Central Lines7 lines

{3, 1132}, {4, 615}, {5, 1131}, {6, 3316}, {226, 1373}, {376, 1328}, {486, 631}

▸ Functional Relations3 relations