X2915

TANGENTIAL-ISOGONAL CONJUGATE OF X1

X2915 is the tangential-isogonal conjugate of X1.
< 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) { 1717, 2960 }: Central Line L(1717, 2960) { 2, 3 }: Euler Line { 35, 37 }: Central Line L(35, 37) { 36, 1104 }: Central Line L(36, 1104) { 511, 1437 }: Central Line L(511, 1437) { 500, 1790 }: Central Line L(500, 1790) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1717 = MIMOSA TRANSFORM OF X(35) (0.6295, 0.3852) X_2960 = EXCENTRAL-ISOGONAL CONJUGATE OF X(155) (0.2435, -0.5134) X_2 = CENTROID (0.5374, 0.2000) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1104 = CROSSPOINT OF X(1) AND X(28) (0.6311, 0.3042) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1437 = -BETH CONJUGATE OF X(283) (0.5584, 0.1373) X_500 = ORTHOCENTER OF THE INCENTRAL TRIANGLE (0.5577, 0.1973) X_1790 = INVERSE MIMOSA TRANSFORM OF X(6) (0.5188, 0.1134) X_2915 = TANGENTIAL-ISOGONAL CONJUGATE OF X(1) (0.4365, -0.0641) A B C X1717 X2960 X2 X3 X35 X37 X36 X1104 X511 X1437 X500 X1790 X2915 (a, b, c) = (5, 6, 7) | AB = 1

X2915 (TANGENTIAL-ISOGONAL CONJUGATE OF X1) 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): \(-65.611122884865\)
▸ Incident Central Lines8 lines

{2, 3}, {35, 37}, {36, 1104}, {40, 2778}, {500, 1790}, {511, 1437}, {1603, 1604}, {1780, 2245}

▸ Functional Relations7 relations

Notes

As a point on the Euler line, X2915 has Shinagawa coefficients \((\$a\$*(E + 2F) + abc, -2\$a\$*(E + F) - abc)\).