X3061

INTERSECTION OF LINES X1X_6 AND X2X_257

X3061 = X3056-cross conjugate of X982
< 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, 6 }: Incenter–Symmedian Line { 2, 257 }: Central Line L(2, 257) { 10, 262 }: Central Line L(10, 262) { 330, 335 }: Central Line L(330, 335) { 39, 986 }: Central Line L(39, 986) { 169, 997 }: Central Line L(169, 997) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_262 = ISOGONAL CONJUGATE OF X(182) (0.5893, 0.2856) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) X_997 = MIDPOINT OF X(1) AND X(200) (0.5053, 0.1685) X_3061 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(257) (0.4848, 0.1304) A B C X1 X6 X2 X257 X10 X262 X330 X335 X39 X986 X169 X997 X3061 (a, b, c) = (5, 6, 7) | AB = 1

X3061 (INTERSECTION OF LINES X1X_6 AND X2X_257) 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 \(f(a,b,c) = (b + c - a)(b^{2} + c^{2} - bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.898256008186\)
▸ Incident Central Lines10 lines

{1, 6}, {2, 257}, {10, 262}, {21, 2344}, {39, 986}, {63, 1429}, {78, 2082}, {169, 997}, {304, 1921}, {330, 335}

▸ Functional Relations6 relations