X3989

X1962com(INCENTRAL TRIANGLE)

< 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) { 37, 38 }: Central Line L(37, 38) { 2, 726 }: Central Line L(2, 726) { 165, 612 }: Central Line L(165, 612) { 45, 748 }: Central Line L(45, 748) { 42, 984 }: Central Line L(42, 984) { 756, 899 }: Central Line L(756, 899) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_2 = CENTROID (0.5374, 0.2000) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_748 = INTERSECTION OF LINES X(2)X(31) AND X(9)X(38) (0.4360, 0.0802) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_756 = CROSSPOINT OF X(10) AND X(37) (0.5409, 0.1988) X_899 = INTERSECTION OF LINES X(1)X(2) AND X(6)X(750) (2.3571, 1.9829) X_3989 = com(INCENTRAL TRIANGLE) (0.5536, 0.2113) A B C X37 X38 X2 X726 X165 X612 X45 X748 X42 X984 X756 X899 X3989 (a, b, c) = (5, 6, 7) | AB = 1

X3989 (X1962com(INCENTRAL 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 \(f(a,b,c) = a(2b^{2} + 2c^{2} + ab + ac + 2bc)\)
Search Value (6, 9, 13): \(2.178979305546\)
▸ Incident Central Lines14 lines

{1, 2308}, {2, 726}, {37, 38}, {42, 984}, {45, 748}, {165, 612}, {517, 2292}, {518, 1962}, {614, 3731}, {756, 899}, {846, 902}, {896, 3745}, {1051, 1757}, {1961, 3218}