X1003

INTERCEPT OF EULER LINE AND LINE X6X_99

X1003 = crossdifference of every pair of points on line X647X888
< 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, 99 }: Central Line L(6, 99) { 183, 187 }: Central Line L(183, 187) { 32, 538 }: Central Line L(32, 538) 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_99 = STEINER POINT (0.1109, 0.4322) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_538 = DIRECTION OF VECTOR AX + BX + CX, where X = X(39) (1.0053, 0.5542) X_1003 = INTERCEPT OF EULER LINE AND LINE X(6)X(99) (0.5673, 0.2782) A B C X2 X3 X4 X6 X99 X183 X187 X32 X538 X1003 (a, b, c) = (5, 6, 7) | AB = 1

X1003 (INTERCEPT OF EULER LINE AND LINE X6X_99) 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 \(f(a,b,c) = bc(3a^{4} - a^{2}b^{2} - a^{2}c^{2} + 2b^{2}c^{2})\)
Search Value (6, 9, 13): \(1.607598592277\)
▸ Incident Central Lines4 lines

{2, 3}, {6, 99}, {32, 538}, {183, 187}

▸ Functional Relations9 relations

Notes

As a point on the Euler line, X1003 has Shinagawa coefficients \(((E + F)^{2} - 2S^{2}, 3S^{2})\).