X966

INTERSECTION OF LINES X2X_6 AND X4X_9

X966 = tripolar centroid of X623
< 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 { 4, 9 }: Orthocenter–Spieker Line { 8, 37 }: Central Line L(8, 37) { 45, 346 }: Central Line L(45, 346) { 443, 579 }: Central Line L(443, 579) { 198, 958 }: Central Line L(198, 958) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_967 = ISOGONAL CONJUGATE OF X(966) (0.6112, 0.2884) X_2 = CENTROID (0.5374, 0.2000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_8 = NAGEL POINT (0.4694, 0.1333) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_346 = ISOTOMIC CONJUGATE OF X(279) (0.3948, 0.0827) X_443 = COMPLEMENT OF X(452) (0.5427, 0.2138) X_579 = HARMONIC OF X(284) (0.7212, 0.4674) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_966 = INTERSECTION OF LINES X(2)X(6) AND X(4)X(9) (0.5191, 0.1803) A B C X967 X2 X6 X4 X9 X8 X37 X45 X346 X443 X579 X198 X958 X966 (a, b, c) = (5, 6, 7) | AB = 1

X966 (INTERSECTION OF LINES X2X_6 AND X4X_9) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(bc[a^{2} - 2a(b + c) - (b + c)^{2}] : :\)
Barycentrics: \(a^{2} - 2s^{2} : :\)
Search Value (6, 9, 13): \(3.155242550986\)
▸ Incident Central Lines10 lines

{2, 6}, {4, 9}, {8, 37}, {45, 346}, {198, 958}, {307, 948}, {374, 3740}, {443, 579}, {572, 631}, {581, 936}

▸ Functional Relations3 relations