X3126

DANNEELS PERSPECTOR FOR X100

X3126 = center of hyperbola {{A, B, C,X11,X100,X650,X693}}
< 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) { 119, 120 }: Central Line L(119, 120) { 9, 513 }: Central Line L(9, 513) { 10, 514 }: Central Line L(10, 514) { 142, 522 }: Central Line L(142, 522) { 3, 667 }: Central Line L(3, 667) { 2, 885 }: Central Line L(2, 885) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_120 = -OF-MEDIAL-TRIANGLE (0.3204, 0.3466) X_9 = MITTENPUNKT (0.5110, 0.1615) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_667 = CROSSDIFFERENCE OF X(2) AND X(37) (-6.1667, 5.7155) X_2 = CENTROID (0.5374, 0.2000) X_885 = ISOTOMIC CONJUGATE OF X(883) (1.0518, 0.0256) X_3126 = DANNEELS PERSPECTOR FOR X(100) (0.2802, 0.2871) A B C X119 X120 X9 X513 X10 X514 X142 X522 X3 X667 X2 X885 X3126 (a, b, c) = (5, 6, 7) | AB = 1

X3126 (DANNEELS PERSPECTOR FOR X100) 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 \(f(a,b,c) = (b - c)(b^{2} + c^{2} - ab - ac)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.286580342695\)
▸ Incident Central Lines12 lines

{1, 905}, {2, 885}, {3, 667}, {9, 513}, {10, 514}, {119, 120}, {142, 522}, {442, 1577}, {650, 1027}, {656, 2092}, {665, 1642}, {1025, 1026}

▸ Functional Relations1 relation