X948

INTERSECTION OF LINES X1X_4 AND X6X_7

X948 = crossdifference of every pair of points on line X652X926
< 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) { 1, 4 }: Incenter–Orthocenter Line { 6, 7 }: Central Line L(6, 7) { 2, 85 }: Central Line L(2, 85) { 57, 169 }: Central Line L(57, 169) { 37, 347 }: Central Line L(37, 347) { 142, 269 }: Central Line L(142, 269) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_949 = ISOGONAL CONJUGATE OF X(948) (0.5571, 0.1869) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_7 = GERGONNE POINT (0.5903, 0.2769) X_2 = CENTROID (0.5374, 0.2000) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_269 = ISOGONAL CONJUGATE OF X(200) (0.6369, 0.3847) X_948 = INTERSECTION OF LINES X(1)X(4) AND X(6)X(7) (0.5840, 0.2831) A B C X949 X1 X4 X6 X7 X2 X85 X57 X169 X37 X347 X142 X269 X948 (a, b, c) = (5, 6, 7) | AB = 1

X948 (INTERSECTION OF LINES X1X_4 AND X6X_7) 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 \(f(a,b,c) = bcvw[a^{3} - a^{2}(b + c) + a(b + c)^{2} - (b - c)(b^{2} - c^{2})]\), where \(u : v : w\) = X9
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(0.649324226899\)
▸ Incident Central Lines9 lines

{1, 4}, {2, 85}, {6, 7}, {37, 347}, {57, 169}, {142, 269}, {220, 329}, {307, 966}, {342, 393}

▸ Functional Relations2 relations