X1472

X1036-BETH CONJUGATE OF X1036

X1472 = isogonal conjugate of X4385
< 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) { 3, 31 }: Central Line L(3, 31) { 32, 48 }: Central Line L(32, 48) { 28, 614 }: Central Line L(28, 614) { 58, 988 }: Central Line L(58, 988) { 104, 1039 }: Central Line L(104, 1039) { 238, 987 }: Central Line L(238, 987) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1036 = ISOGONAL CONJUGATE OF X(388) (0.5632, 0.2044) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_614 = INTERSECTION OF LINES X(1)X(2) AND X(11)X(33) (0.6310, 0.2916) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_988 = INTERSECTION OF LINES X(1)X(3) AND X(9)X(39) (0.5598, 0.2120) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_1039 = ISOGONAL CONJUGATE OF X(1038) (0.6094, 0.3672) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_987 = ISOGONAL CONJUGATE OF X(986) (0.5829, 0.2572) X_1472 = -BETH CONJUGATE OF X(1036) (0.6306, 0.3134) A B C X1036 X3 X31 X32 X48 X28 X614 X58 X988 X104 X1039 X238 X987 X1472 (a, b, c) = (5, 6, 7) | AB = 1

X1472 (X1036-BETH CONJUGATE OF X1036) 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 \(f(a,b,c) = (1 - \cos A)u(a,b,c)\), where \(u : v : w\) = X1036
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.428826489883\)
▸ Incident Central Lines10 lines

{3, 31}, {28, 614}, {32, 48}, {56, 1395}, {58, 988}, {104, 1039}, {238, 987}, {595, 997}, {603, 1397}, {727, 1310}

▸ Functional Relations1 relation

  • X1472 = isogonal conjugate of X4385