X3055

{X2,X6}-HARMONIC CONJUGATE OF X3054

X3055 is the {X2,X6}-harmonic conjugate of X3054.
< 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) { 2, 6 }: Centroid–Symmedian Line { 140, 187 }: Central Line L(140, 187) { 5, 574 }: Central Line L(5, 574) { 115, 547 }: Central Line L(115, 547) { 32, 632 }: Central Line L(32, 632) { 570, 2493 }: Central Line L(570, 2493) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_574 = HARMONIC OF X(187) (0.5539, 0.1910) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_547 = MIDPOINT OF X(2) AND X(5) (0.5468, 0.2244) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_632 = 9/10*OG (0.5337, 0.1902) X_570 = ORTHOGONAL OF X(52) (0.5652, 0.2098) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (-0.6894, 1.3058) X_3055 = {X(2),X(6)}-HARMONIC CONJUGATE OF X(3054) (0.5549, 0.2188) A B C X2 X6 X140 X187 X5 X574 X115 X547 X32 X632 X570 X2493 X3055 (a, b, c) = (5, 6, 7) | AB = 1

X3055 ({X2,X6}-HARMONIC CONJUGATE OF X3054) 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 \(f(a,b,c) = bc(2a^{4} + 3b^{4} + 3c^{4} - 7a^{2}b^{2} - 7a^{2}c^{2} - 6b^{2}c^{2})\)
Barycentrics: \(12\sigma + a^{2}\cot \omega : 12\sigma + b^{2}\cot \omega : 12\sigma + c^{2}\cot \omega\)
Search Value (6, 9, 13): \(1.805315586992\)
▸ Incident Central Lines7 lines

{2, 6}, {5, 574}, {32, 632}, {115, 547}, {140, 187}, {570, 2493}, {1384, 2548}

▸ Functional Relations4 relations