X3552

EULER LINE INTERCEPT OF LINE X32X_99

X3552 = cevapoint of X3 and X3360
< 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 { 32, 99 }: Central Line L(32, 99) { 76, 187 }: Central Line L(76, 187) { 172, 192 }: Central Line L(172, 192) { 83, 574 }: Central Line L(83, 574) { 287, 1204 }: Central Line L(287, 1204) 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_32 = 3rd POWER POINT (0.6400, 0.3332) X_99 = STEINER POINT (0.1109, 0.4322) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_172 = TRILINEAR PRODUCT X(6)*X(171) (0.6080, 0.2866) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_287 = -HIRST INVERSE OF X(98) (0.7437, -0.0511) X_1204 = 3rd SARAGOSSA POINT OF X(64) (0.6497, 0.1923) X_3552 = EULER LINE INTERCEPT OF LINE X(32)X(99) (0.5918, 0.3423) A B C X2 X3 X4 X32 X99 X76 X187 X172 X192 X83 X574 X287 X1204 X3552 (a, b, c) = (5, 6, 7) | AB = 1

X3552 (EULER LINE INTERCEPT OF LINE X32X_99) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc(2a^{4} + b^{2}c^{2} - c^{2}a^{2} - a^{2}b^{2}) : :\)
Search Value (6, 9, 13): \(1.145298872003\)
▸ Incident Central Lines10 lines

{2, 3}, {32, 99}, {69, 2076}, {76, 187}, {83, 574}, {172, 192}, {287, 1204}, {330, 1914}, {385, 1975}, {1613, 3360}

▸ Functional Relations10 relations

Notes

As a point on the Euler line, X3552 has Shinagawa coefficients \(((E + F)^{2} - 3S^{2}, 4S^{2})\).