X1150

INTERSECTION OF LINES X2X_6 AND X3X_8

X1150 = complement of X31034
< 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 { 3, 8 }: Central Line L(3, 8) { 63, 321 }: Central Line L(63, 321) { 88, 330 }: Central Line L(88, 330) { 10, 750 }: Central Line L(10, 750) { 76, 799 }: Central Line L(76, 799) 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_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_330 = ISOTOMIC CONJUGATE OF X(192) (0.4364, 0.1391) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_1150 = INTERSECTION OF LINES X(2)X(6) AND X(3)X(8) (0.4725, 0.1302) A B C X2 X6 X3 X8 X63 X321 X88 X330 X10 X750 X76 X799 X1150 (a, b, c) = (5, 6, 7) | AB = 1

X1150 (INTERSECTION OF LINES X2X_6 AND X3X_8) 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 \(f(a,b,c) = (b^{2} + c^{2} - a^{2}) + bc(b + c)/a\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(4.617953627354\)
▸ Incident Central Lines8 lines

{2, 6}, {3, 8}, {10, 750}, {58, 964}, {63, 321}, {76, 799}, {88, 330}, {239, 980}

▸ Functional Relations2 relations