X996

INTERSECTION OF LINES X8X_58 AND X10X_56

X996 = trilinear pole of line X649X900
< 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) { 8, 58 }: Central Line L(8, 58) { 10, 56 }: Central Line L(10, 56) { 2, 106 }: Central Line L(2, 106) { 6, 519 }: Central Line L(6, 519) { 182, 952 }: Central Line L(182, 952) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_995 = MIDPOINT OF X(1) AND X(43) (0.6036, 0.2648) X_8 = NAGEL POINT (0.4694, 0.1333) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_2 = CENTROID (0.5374, 0.2000) X_106 = Λ(INCENTER, CENTROID) (1.0000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_952 = INTERSECTION OF X(1)X(5) AND X(3)X(8) (0.1267, 0.6191) X_996 = INTERSECTION OF LINES X(8)X(58) AND X(10)X(56) (0.5332, 0.2018) A B C X995 X8 X58 X10 X56 X2 X106 X6 X519 X182 X952 X996 (a, b, c) = (5, 6, 7) | AB = 1

X996 (INTERSECTION OF LINES X8X_58 AND X10X_56) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(1/[a(ab + ac - bc + b^{2} + c^{2})] : :\)
Search Value (6, 9, 13): \(2.704746908115\)
▸ Incident Central Lines5 lines

{2, 106}, {6, 519}, {8, 58}, {10, 56}, {182, 952}

▸ Functional Relations3 relations