X980

INTERSECTION OF LINES X1X_3 AND X2X_39

X980 = crossdifference of every pair of points on line X650X669
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 2, 39 }: Central Line L(2, 39) { 32, 81 }: Central Line L(32, 81) { 63, 213 }: Central Line L(63, 213) { 38, 869 }: Central Line L(38, 869) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_981 = ISOGONAL CONJUGATE OF X(980) (0.5781, 0.2464) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_980 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(39) (0.5644, 0.2204) A B C X981 X1 X3 X2 X39 X32 X81 X63 X213 X38 X869 X980 (a, b, c) = (5, 6, 7) | AB = 1

X980 (INTERSECTION OF LINES X1X_3 AND X2X_39) 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 \(f(a,b,c) = a^{2}(b^{2} + bc + c^{2}) + (b^{2} + c^{2})(bc + ca + ab)\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.906943083314\)
▸ Incident Central Lines5 lines

{1, 3}, {2, 39}, {32, 81}, {38, 869}, {63, 213}

▸ Functional Relations2 relations