X1330

ANTICOMPLEMENTARY CONJUGATE OF X1

X1330 = reflection of X1046 in X10
< 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) { 1046, 10 }: Central Line L(1046, 10) { 2, 58 }: Central Line L(2, 58) { 4, 69 }: Central Line L(4, 69) { 8, 79 }: Central Line L(8, 79) { 193, 387 }: Central Line L(193, 387) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2 = CENTROID (0.5374, 0.2000) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_8 = NAGEL POINT (0.4694, 0.1333) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_193 = -CEVA CONJUGATE OF X(2) (0.7878, 0.4690) X_387 = INTERSECTION OF LINES X(1,2) AND X(4,6) (0.5994, 0.2607) X_1330 = ANTICOMPLEMENTARY CONJUGATE OF X(1) (0.3908, 0.0300) A B C X1046 X10 X2 X58 X4 X69 X8 X79 X193 X387 X1330 (a, b, c) = (5, 6, 7) | AB = 1

X1330 (ANTICOMPLEMENTARY CONJUGATE OF X1) 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 \(f(a,b,c) = bc[b^{2}/(a + c) + c^{2}/(a + b) - a^{2}/(b + c)]\)
Barycentrics: \((c^{2} + a^{2} - b^{2}) (a^{2} + b^{2} - c^{2}) - (b^{2} + c^{2} - a^{2}) (a + b + c)^{2} : :\)
Search Value (6, 9, 13): \(6.384241886742\)
▸ Incident Central Lines9 lines

{2, 58}, {4, 69}, {8, 79}, {10, 894}, {30, 1043}, {193, 387}, {320, 942}, {333, 442}, {1010, 1211}

▸ Functional Relations6 relations