X3497

ISOGONAL CONJUGATE OF X3496

X3497 is the isogonal conjugate of X3496.
< 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) { 257, 384 }: Central Line L(257, 384) { 3, 984 }: Central Line L(3, 984) { 607, 2221 }: Central Line L(607, 2221) { 63, 2896 }: Central Line L(63, 2896) { 1, 3492 }: Central Line L(1, 3492) { 3491, 3494 }: Central Line L(3491, 3494) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_1 = INCENTER (0.5714, 0.2333) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_607 = ISOGONAL CONJUGATE OF X(348) (0.6187, 0.3865) X_2221 = -ISOCONJUGATE OF X(612) (0.6101, 0.2802) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4820, 0.1279) X_3492 = INTERSECTION OF LINES X(4)X(83) AND X(32)X(695) (0.5108, 0.0518) X_3491 = INTERSECTION OF LINES X(1)X(295) AND X(4)X(69) (0.5262, 0.2536) X_3494 = INTERSECTION OF LINES X(1)X(87) AND X(3)X(2053) (0.4381, 0.1402) X_3497 = ISOGONAL CONJUGATE OF X(3496) (0.6174, 0.3711) A B C X172 X1 X257 X384 X3 X984 X607 X2221 X63 X2896 X3492 X3491 X3494 X3497 (a, b, c) = (5, 6, 7) | AB = 1

X3497 (ISOGONAL CONJUGATE OF X3496) 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 \(f(a,b,c) = 1\)(\(b^{3}\) + \(c^{3}\) - \(a^{3}\) + abc) (E. Danneels)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.766118249825\)

X3497 lies on the cubic Z(X384).

▸ Incident Central Lines6 lines

{1, 3492}, {3, 984}, {63, 2896}, {257, 384}, {607, 2221}, {3491, 3494}

▸ Functional Relations3 relations