X3337

INTERSECTION OF LINES X1X_3 AND X7X_499

< 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) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 11, 79 }: Central Line L(11, 79) { 58, 229 }: Central Line L(58, 229) { 7, 499 }: Central Line L(7, 499) { 81, 501 }: Central Line L(81, 501) { 47, 1471 }: Central Line L(47, 1471) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_229 = -CEVA CONJUGATE OF X(81) (0.5961, 0.2991) X_7 = GERGONNE POINT (0.5903, 0.2769) X_499 = {X(1),X(2)}-HARMONIC CONJUGATE OF X(498) (0.4458, 0.1102) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_501 = MIQUEL ASSOCIATE OF INCENTER (0.5444, 0.1612) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_1471 = -BETH CONJUGATE OF X(1001) (0.6167, 0.3077) X_3337 = INTERSECTION OF LINES X(1)X(3) AND X(7)X(499) (0.6034, 0.2920) A B C X1 X3 X11 X79 X58 X229 X7 X499 X81 X501 X47 X1471 X3337 (a, b, c) = (5, 6, 7) | AB = 1

X3337 (INTERSECTION OF LINES X1X_3 AND X7X_499) 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 \(f(a,b,c) = (a - b + c)(a + b - c)(a + b + c) + abc\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.668705121923\)
▸ Incident Central Lines12 lines

{1, 3}, {7, 499}, {11, 79}, {47, 1471}, {58, 229}, {81, 501}, {202, 2306}, {553, 1776}, {946, 1768}, {1111, 1434}, {1399, 1421}, {1731, 1781}