X2918

TANGENTIAL-ISOGONAL CONJUGATE OF X5

X2918 is the tangential-isogonal conjugate of X5.
< 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) { 6, 26 }: Central Line L(6, 26) { 22, 155 }: Central Line L(22, 155) { 184, 195 }: Central Line L(184, 195) { 1351, 2916 }: Central Line L(1351, 2916) { 550, 2935 }: Central Line L(550, 2935) { 1658, 2929 }: Central Line L(1658, 2929) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE (0.1382, -0.8447) X_22 = EXETER POINT (0.4143, -0.1221) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_1351 = REFLECTION OF X(3) IN X(6) (0.7000, 0.4324) X_2916 = TANGENTIAL-ISOGONAL CONJUGATE OF X(2) (0.4656, -0.0146) X_550 = MIDPOINT OF X(3) AND X(20) (0.4439, -0.0448) X_2935 = TANGENTIAL-ISOGONAL CONJUGATE OF X(186) (0.0611, 2.4859) X_1658 = CIRCUMCENTER OF KOSNITA TRIANGLE (0.3191, -0.3713) X_2929 = TANGENTIAL-ISOGONAL CONJUGATE OF X(20) (0.6368, 0.3026) X_2918 = TANGENTIAL-ISOGONAL CONJUGATE OF X(5) (0.4510, -0.0916) A B C X5 X6 X26 X22 X155 X184 X195 X1351 X2916 X550 X2935 X1658 X2929 X2918 (a, b, c) = (5, 6, 7) | AB = 1

X2918 (TANGENTIAL-ISOGONAL CONJUGATE OF X5) 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) is as described just before X2883
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-6.417301084893\)
▸ Incident Central Lines6 lines

{6, 26}, {22, 155}, {184, 195}, {550, 2935}, {1351, 2916}, {1658, 2929}