X2973

7th MACBEATH POINT

X2973 = cevapoint of X1986 and X2969
< 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) { 4, 150 }: Central Line L(4, 150) { 25, 675 }: Central Line L(25, 675) { 3, 917 }: Central Line L(3, 917) { 1235, 1969 }: Central Line L(1235, 1969) { 1565, 2969 }: Central Line L(1565, 2969) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1986 = HATZIPOLAKIS REFLECTION POINT (0.5352, 0.5340) X_2969 = 3rd MACBEATH POINT (0.7614, 0.2435) X_4 = ORTHOCENTER (0.6122, 0.3958) X_150 = REFLECTION OF X(20) IN X(103) (1.1837, -0.4499) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_675 = TRILINEAR POLE OF LINE X(6)X(514) (0.9212, -0.1860) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_917 = -CROSS CONJUGATE OF X(4) (0.9795, 0.2766) X_1235 = ISOTOMIC CONJUGATE OF X(1176) (0.5483, 0.2901) X_1969 = TRILINEAR PRODUCT OF PU(38) (0.5432, 0.2926) X_1565 = ORTHOJOIN OF X(657) (0.7114, 0.0321) X_2973 = 7th MACBEATH POINT (0.7494, 0.1928) A B C X1986 X2969 X4 X150 X25 X675 X3 X917 X1235 X1969 X1565 X2973 (a, b, c) = (5, 6, 7) | AB = 1

X2973 (7th MACBEATH POINT) 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 \(f(a,b,c) = [bc(b - c)]^{2}\cos B \cos C\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.762039952324\)
▸ Incident Central Lines5 lines

{3, 917}, {4, 150}, {25, 675}, {1235, 1969}, {1565, 2969}

▸ Functional Relations5 relations