X1975

CROSSSUM OF PU(39)

X1975 = midpoint of X489 and X490
< 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) { 489, 490 }: Central Line L(489, 490) { 3, 76 }: Central Line L(3, 76) { 20, 64 }: Central Line L(20, 64) { 6, 194 }: Central Line L(6, 194) { 4, 325 }: Central Line L(4, 325) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_489 = CEVAPOINT OF X(20) AND X(487) (0.4404, 0.3605) X_490 = CEVAPOINT OF X(20) AND X(488) (0.4037, -0.0241) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_4 = ORTHOCENTER (0.6122, 0.3958) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_1975 = CROSSSUM OF PU(39) (0.4220, 0.1682) A B C X489 X490 X3 X76 X20 X64 X6 X194 X4 X325 X1975 (a, b, c) = (5, 6, 7) | AB = 1

X1975 (CROSSSUM OF PU(39)) 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 \(f(a,b,c) = \cos B \cos C + (bc \cos^{2} A)/a^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.261370884460\)
▸ Incident Central Lines19 lines

{3, 76}, {4, 325}, {6, 194}, {20, 64}, {25, 305}, {30, 315}, {32, 538}, {56, 350}, {75, 958}, {190, 220}, {221, 664}, {264, 1105}, {274, 405}, {310, 1011}, {316, 382}, {378, 1235}, {394, 401}, {543, 626}, {801, 1073}

▸ Functional Relations10 relations