X2592

X6-ISOCONJUGATE OF X1822

X2592 = polar conjugate of X1113
< 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) { 297, 525 }: Central Line L(297, 525) { 98, 1114 }: Central Line L(98, 1114) { 262, 1346 }: Central Line L(262, 1346) { 4, 2574 }: Central Line L(4, 2574) { 10, 2588 }: Central Line L(10, 2588) { 226, 2582 }: Central Line L(226, 2582) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_297 = -HIRST INVERSE OF X(4) (0.8440, 1.0022) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_98 = TARRY POINT (0.8891, -0.2281) X_1114 = 2nd EULER-LINE-CIRCUMCIRCLE INTERSECTION (0.3178, -0.3746) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_1346 = INSIMILICENTER(NINE-POINT CIRCLE, ORTHOCENTROIDAL CIRCLE) (0.5694, 0.2836) X_4 = ORTHOCENTER (0.6122, 0.3958) X_2574 = ISOGONAL CONJUGATE OF X(1113) (-0.0479, 0.1579) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2588 = -ISOCONJUGATE OF X(1113) (2.4671, 0.4270) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_2582 = -ISOCONJUGATE OF X(1113) (-4.3713, -0.2718) X_2592 = -ISOCONJUGATE OF X(1822) (4.3749, 0.6658) A B C X297 X525 X98 X1114 X262 X1346 X4 X2574 X10 X2588 X226 X2582 X2592 (a, b, c) = (5, 6, 7) | AB = 1

X2592 (X6-ISOCONJUGATE OF X1822) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc/f(a,b,c) : ca/f(b,c,a) : ab/f(c,a,b)\), where f(a,b,c) is as at X1822
Barycentrics: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\)
Search Value (6, 9, 13): \(-58.736479851547\)

X2592 lies on the Kiepert hyperbola.

▸ Incident Central Lines6 lines

{4, 2574}, {10, 2588}, {98, 1114}, {226, 2582}, {262, 1346}, {297, 525}

▸ Functional Relations4 relations