X3999

X899com(INTOUCH TRIANGLE)

X3999 = incircle-inverse of X34583
< 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) incircle: Incircle of △ABC { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 244, 518 }: Central Line L(244, 518) { 88, 1280 }: Central Line L(88, 1280) { 44, 3290 }: Central Line L(44, 3290) { 38, 3742 }: Central Line L(38, 3742) { 896, 3246 }: Central Line L(896, 3246) 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_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_1280 = ISOGONAL CONJUGATE OF X(1279) (1.1600, 0.1306) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_3290 = INTERSECTION OF LINES X(2)X(37) AND X(230)X(231) (1.0664, 0.6348) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_3742 = com[n(INCENTRAL)*n(MEDIAL)] (0.5599, 0.2266) X_896 = INTERSECTION OF LINES X(1)X(21) AND X(9)X(750) (2.0357, 2.1579) X_3246 = MIDPOINT OF X(1) AND X(44) (1.3571, 1.1664) X_3999 = com(INTOUCH TRIANGLE) (0.0000, -0.8165) A B C X1 X3 X244 X518 X88 X1280 X44 X3290 X38 X3742 X896 X3246 X3999 (a, b, c) = (5, 6, 7) | AB = 1

X3999 (X899com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(3b^{2} + 3c^{2} - ab - ac - 4bc)\)
Search Value (6, 9, 13): \(5.427596131284\)
▸ Incident Central Lines13 lines

{1, 3}, {38, 3742}, {44, 3290}, {88, 1280}, {244, 518}, {896, 3246}, {908, 3756}, {1054, 3689}, {1279, 3218}, {3240, 3752}, {3242, 3306}, {3667, 3676}, {3693, 3726}

▸ Functional Relations1 relation

  • X3999 = incircle-inverse of X34583