X2669

CROSSDIFFERENCE OF PU(85)

X2669 = perspector of conic {A, B, C,PU(84)}
< 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, 75 }: Central Line L(1, 75) { 99, 238 }: Central Line L(99, 238) { 42, 873 }: Central Line L(42, 873) { 799, 899 }: Central Line L(799, 899) { 798, 1019 }: Central Line L(798, 1019) { 1434, 1469 }: Central Line L(1434, 1469) 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_1 = INCENTER (0.5714, 0.2333) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_99 = STEINER POINT (0.1109, 0.4322) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_873 = ISOGONAL CONJUGATE OF X(872) (0.5339, 0.2011) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_899 = INTERSECTION OF LINES X(1)X(2) AND X(6)X(750) (2.3571, 1.9829) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_1019 = -CEVA CONJUGATE OF X(1) (-29.0952, 18.1962) X_1434 = -BETH CONJUGATE OF X(274) (0.6014, 0.2949) X_1469 = -BETH CONJUGATE OF X(984) (0.6171, 0.3088) X_2669 = CROSSDIFFERENCE OF PU(85) (3.1271, 2.5227) A B C X2 X1 X75 X99 X238 X42 X873 X799 X899 X798 X1019 X1434 X1469 X2669 (a, b, c) = (5, 6, 7) | AB = 1

X2669 (CROSSDIFFERENCE OF PU(85)) 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 \(f(a,b,c) = a^{2}bc/[(a + b)(a + c)] - [bc/(b + c)]^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-11.631410372276\)
▸ Incident Central Lines6 lines

{1, 75}, {42, 873}, {99, 238}, {798, 1019}, {799, 899}, {1434, 1469}

▸ Functional Relations3 relations