X3079

DANNEELS POINT OF X20

X3079 = X20-Ceva conjugate of X1249
< 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) { 2, 3 }: Euler Line { 154, 1249 }: Central Line L(154, 1249) { 204, 1394 }: Central Line L(204, 1394) { 459, 1503 }: Central Line L(459, 1503) { 1498, 2131 }: Central Line L(1498, 2131) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_20 = DE LONGCHAMPS POINT (0.3878, -0.1916) X_1249 = ISOGONAL CONJUGATE OF X(1073) (-0.9482, -15.9845) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_204 = -CEVA CONJUGATE OF X(19) (0.6683, 3.3982) X_1394 = -BETH CONJUGATE OF X(20) (0.4977, -0.6923) X_459 = -CEVA CONJUGATE OF X(4) (0.5934, 0.8103) X_1503 = POINT ARKAB (0.4818, -0.3843) X_1498 = REFLECTION OF X(64) IN X(3) (0.4421, -1.3902) X_2131 = ISOGONAL CONJUGATE OF X(2130) (0.5325, 0.1568) X_3079 = DANNEELS POINT OF X(20) (0.5346, 0.1926) A B C X20 X1249 X2 X3 X154 X204 X1394 X459 X1503 X1498 X2131 X3079 (a, b, c) = (5, 6, 7) | AB = 1

X3079 (DANNEELS POINT OF X20) 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 \(f(a,b,c) = a u^{2}(bv + cw)\), where \(u : v : w\) = X20
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\) As a point on the Euler line, X3079 has Shinagawa coefficients \((4F^{2}, -4(E + F)F + S^{2})\).
Search Value (6, 9, 13): \(-0.644259308074\)
▸ Incident Central Lines7 lines

{2, 3}, {154, 1249}, {204, 1394}, {459, 1503}, {1495, 6524}, {1498, 2131}, {5562, 5910}

▸ Functional Relations2 relations