X1889

ZOSMA TRANSFORM OF X968

X1889 = inverse-in-orthocentroidal-circle of X430
< 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) { 2, 3 }: Euler Line { 6, 1836 }: Central Line L(6, 1836) { 518, 1824 }: Central Line L(518, 1824) { 1709, 1730 }: Central Line L(1709, 1730) { 57, 1893 }: Central Line L(57, 1893) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_1836 = ZOSMA TRANSFORM OF X(33) (0.6066, 0.3254) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_1824 = ZOSMA TRANSFORM OF X(2) (0.6198, 0.4097) X_1709 = MIMOSA TRANSFORM OF X(9) (0.5826, 0.3739) X_1730 = MIMOSA TRANSFORM OF X(86) (0.6546, 0.4410) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1893 = ZOSMA TRANSFORM OF X(991) (0.6159, 0.4157) X_1889 = ZOSMA TRANSFORM OF X(968) (0.6157, 0.4048) A B C X2 X3 X4 X6 X1836 X518 X1824 X1709 X1730 X57 X1893 X1889 (a, b, c) = (5, 6, 7) | AB = 1

X1889 (ZOSMA TRANSFORM OF X968) 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,\(x : y : z\) = X968
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X968
Search Value (6, 9, 13): \(-3.476257044300\)
▸ Incident Central Lines5 lines

{2, 3}, {6, 1836}, {57, 1893}, {518, 1824}, {1709, 1730}

▸ Functional Relations1 relation

  • X1889 = inverse-in-orthocentroidal-circle of X430

Notes

As a point on the Euler line, X1889 has Shinagawa coefficients \((F, -E - F - 2\$bc\$)\).