X3002

(BROCARD AXIS)∩(GERGONNE LINE)

X3002 = crosssum of X6 and X851
< 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) { 3, 6 }: Brocard Axis { 241, 514 }: Central Line L(241, 514) { 36, 1951 }: Central Line L(36, 1951) { 978, 1047 }: Central Line L(978, 1047) { 1758, 1945 }: Central Line L(1758, 1945) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1951 = CROSSDIFFERENCE OF PU(20) (3.2396, 6.6676) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_1047 = -CEVA CONJUGATE OF X(1) (0.5281, -0.0076) X_1758 = MIMOSA TRANSFORM OF X(296) (1.1982, 1.3847) X_1945 = TRILINEAR POLE OF PU(18) (0.9520, -0.5335) X_3002 = (BROCARD AXIS)∩(GERGONNE LINE) (1.1771, 1.2203) A B C X3 X6 X241 X514 X36 X1951 X978 X1047 X1758 X1945 X3002 (a, b, c) = (5, 6, 7) | AB = 1

X3002 ((BROCARD AXIS)∩(GERGONNE LINE)) 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 \(f(A,B,C) = \sin(A - B) \cos^{2}(B/2) + \sin(A - C) \cos^{2}(C/2)\)
Barycentrics: \((\sin A)f(A,B,C)) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-1.062688932867\)
▸ Incident Central Lines5 lines

{3, 6}, {36, 1951}, {241, 514}, {978, 1047}, {1758, 1945}

▸ Functional Relations2 relations