X2931

TANGENTIAL-ISOGONAL CONJUGATE OF X30

X2931 is the tangential-isogonal conjugate of X30.
< 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) { 155, 110 }: Central Line L(155, 110) { 22, 74 }: Central Line L(22, 74) { 3, 125 }: Central Line L(3, 125) { 24, 110 }: Central Line L(24, 110) { 25, 113 }: Central Line L(25, 113) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_155 = EIGENCENTER OF ORTHIC TRIANGLE (1.1658, 0.5033) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_22 = EXETER POINT (0.4143, -0.1221) X_74 = ISOGONAL CONJUGATE OF EULER INFINITY POINT (0.7484, -0.3437) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_2931 = TANGENTIAL-ISOGONAL CONJUGATE OF X(30) (-0.6626, 0.5924) A B C X155 X110 X22 X74 X3 X125 X24 X25 X113 X2931 (a, b, c) = (5, 6, 7) | AB = 1

X2931 (TANGENTIAL-ISOGONAL CONJUGATE OF X30) 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): \(2.079446368502\)

X2931 lies on the tangential circle, the Walsmith rectangular hyperbola.

▸ Incident Central Lines15 lines

{3, 125}, {6, 1511}, {22, 74}, {23, 146}, {24, 110}, {25, 113}, {26, 1498}, {30, 2935}, {68, 1658}, {110, 895}, {159, 542}, {186, 3580}, {195, 568}, {399, 1495}, {912, 2948}

▸ Functional Relations6 relations