X2969

3rd MACBEATH POINT

X2969 = X1015-cross conjugate of X1086
< 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) { 25, 105 }: Central Line L(25, 105) { 4, 145 }: Central Line L(4, 145) { 124, 136 }: Central Line L(124, 136) { 92, 427 }: Central Line L(92, 427) { 19, 583 }: Central Line L(19, 583) { 242, 468 }: Central Line L(242, 468) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_4 = ORTHOCENTER (0.6122, 0.3958) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_124 = -OF-MEDIAL-TRIANGLE (0.6243, 0.0030) X_136 = INTERSECTION OF LINE X(4)X(110) AND X(25)X(132) (0.8024, 0.3155) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_427 = COMPLEMENT OF X(22) (0.5990, 0.3610) X_19 = CLAWSON POINT (0.6246, 0.4244) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_468 = -LINE CONJUGATE OF X(3) (0.7498, 0.7558) X_2969 = 3rd MACBEATH POINT (0.7614, 0.2435) A B C X25 X105 X4 X145 X124 X136 X92 X427 X19 X583 X242 X468 X2969 (a, b, c) = (5, 6, 7) | AB = 1

X2969 (3rd 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 \(f(a,b,c) = (b - c)^{2}\cos B \cos C\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.986739186825\)

X2969 lies on the orthic inconic.

▸ Incident Central Lines18 lines

{3, 915}, {4, 145}, {19, 583}, {25, 105}, {34, 1411}, {92, 427}, {124, 136}, {125, 1146}, {225, 1828}, {242, 468}, {407, 1829}, {430, 1848}, {867, 2968}, {1118, 1398}, {1565, 2973}, {1785, 1878}, {1824, 1830}, {1870, 1884}

▸ Functional Relations8 relations