X2917

TANGENTIAL-ISOGONAL CONJUGATE OF X4

X2917 is the tangential-isogonal conjugate of X4.
< 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, 24 }: Central Line L(6, 24) { 49, 52 }: Central Line L(49, 52) { 3, 161 }: Central Line L(3, 161) { 26, 154 }: Central Line L(26, 154) { 22, 1498 }: Central Line L(22, 1498) { 68, 1658 }: Central Line L(68, 1658) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_49 = CENTER OF SINE-TRIPLE-ANGLE CIRCLE (0.6275, 0.1789) X_52 = ORTHOCENTER OF ORTHIC TRIANGLE (0.7155, 0.4580) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_161 = -OF-TANGENTIAL-TRIANGLE (0.2845, -1.4852) X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE (0.1382, -0.8447) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_22 = EXETER POINT (0.4143, -0.1221) X_1498 = REFLECTION OF X(64) IN X(3) (0.4421, -1.3902) X_68 = PRASOLOV POINT (-0.0535, -0.0055) X_1658 = CIRCUMCENTER OF KOSNITA TRIANGLE (0.3191, -0.3713) X_2917 = TANGENTIAL-ISOGONAL CONJUGATE OF X(4) (0.4220, -0.4724) A B C X4 X6 X24 X49 X52 X3 X161 X26 X154 X22 X1498 X68 X1658 X2917 (a, b, c) = (5, 6, 7) | AB = 1

X2917 (TANGENTIAL-ISOGONAL CONJUGATE OF X4) 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): \(7.147457134692\)
▸ Incident Central Lines12 lines

{3, 161}, {6, 24}, {20, 2935}, {22, 1498}, {26, 154}, {49, 52}, {68, 1658}, {159, 2934}, {186, 2929}, {343, 1601}, {399, 2937}, {1503, 2916}

▸ Functional Relations4 relations