X1847

ZOSMA TRANSFORM OF X170

X1847 = polar conjugate of X200
< 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, 7 }: Central Line L(4, 7) { 85, 92 }: Central Line L(85, 92) { 278, 279 }: Central Line L(278, 279) { 224, 664 }: Central Line L(224, 664) { 27, 1088 }: Central Line L(27, 1088) { 158, 1111 }: Central Line L(158, 1111) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1802 = INVERSE MIMOSA TRANSFORM OF X(170) (0.3991, 0.0470) X_4 = ORTHOCENTER (0.6122, 0.3958) X_7 = GERGONNE POINT (0.5903, 0.2769) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_278 = ISOGONAL CONJUGATE OF X(219) (0.6278, 0.4577) X_279 = ISOGONAL CONJUGATE OF X(220) (0.6236, 0.3540) X_224 = -CEVA CONJUGATE OF X(63) (1.2479, 0.4419) X_664 = TRILINEAR POLE OF LINE X(2)X(7) (0.2391, 0.5142) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_1088 = TRILINEAR SQUARE OF X(7) (0.6052, 0.3210) X_158 = -CROSS CONJUGATE OF X(92) (0.6215, 0.5117) X_1111 = TRILINEAR SQUARE OF X(514) (0.7470, 0.0849) X_1847 = ZOSMA TRANSFORM OF X(170) (0.6290, 0.4862) A B C X1802 X4 X7 X85 X92 X278 X279 X224 X664 X27 X1088 X158 X1111 X1847 (a, b, c) = (5, 6, 7) | AB = 1

X1847 (ZOSMA TRANSFORM OF X170) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X170
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X170
Search Value (6, 9, 13): \(-0.067066179948\)
▸ Alternate Coordinates1 form

  • Trilinears: \((\tan A)/(1 + \cos A)^{2} : (\tan B)/(1 + \cos B)^{2} : (\tan C)/(1 + \cos C)^{2}\) (M. Iliev, 4/12/07)

▸ Incident Central Lines7 lines

{4, 7}, {27, 1088}, {85, 92}, {158, 1111}, {224, 664}, {278, 279}, {917, 934}

▸ Functional Relations4 relations