X452

X2-HIRST INVERSE OF X449

X452 is the X2-hirst inverse of X449.
< A B C >: Reference Triangle △ABC < K_a K_b K_c >: Anticomplementary Triangle △K_a K_b K_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 443 }: Euler Line { 2, 3 }: Euler Line { 8, 9 }: Central Line L(8, 9) { 72, 145 }: Central Line L(72, 145) { 1, 329 }: Central Line L(1, 329) { 34, 347 }: Central Line L(34, 347) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) K_a = Anticomplementary Vertex K_a (1.6122, 0.5999) K_b = Anticomplementary Vertex K_b (-0.3878, 0.5999) K_c = Anticomplementary Vertex K_c (0.3878, -0.5999) X_2 = CENTROID (0.5374, 0.2000) X_443 = COMPLEMENT OF X(452) (0.5427, 0.2138) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_9 = MITTENPUNKT (0.5110, 0.1615) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_1 = INCENTER (0.5714, 0.2333) X_329 = ISOTOMIC CONJUGATE OF X(189) (0.3847, -0.0222) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_347 = ISOTOMIC CONJUGATE OF X(280) (0.4531, -0.0404) X_452 = -HIRST INVERSE OF X(449) (0.5268, 0.1722) A B C Ka Kb Kc X2 X443 X3 X8 X9 X72 X145 X1 X329 X34 X347 X452 (a, b, c) = (5, 6, 7) | AB = 1

X452 (X2-HIRST INVERSE OF X449) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(u \csc A : v \csc B : w \csc C\), where \(u : v : w\) = X380
Barycentrics: \(u : v : w\)
Search Value (6, 9, 13): \(3.237309374623\)
▸ Incident Central Lines10 lines

{1, 329}, {2, 3}, {8, 9}, {34, 347}, {63, 938}, {72, 145}, {388, 1001}, {392, 944}, {497, 958}, {956, 1058}

▸ Functional Relations3 relations

Notes

As a point on the Euler line, X452 has Shinagawa coefficients \((abc \$a\$ + S^{2},-2S^{2})\).