X3970

X1334com[INVERSE(n(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) { 1, 6 }: Incenter–Symmedian Line { 65, 1018 }: Central Line L(65, 1018) { 55, 1759 }: Central Line L(55, 1759) { 758, 1334 }: Central Line L(758, 1334) { 321, 1930 }: Central Line L(321, 1930) { 79, 2795 }: Central Line L(79, 2795) 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_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_1018 = -CROSS CONJUGATE OF X(1) (0.1051, 0.4358) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1759 = MIMOSA TRANSFORM OF X(304) (0.4099, -0.0023) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_1334 = POINT ALYA (0.5324, 0.1760) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_1930 = BICENTRIC SUM OF PU(14) (0.4644, 0.1374) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_2795 = ISOGONAL CONJUGATE OF X(2711) (1.0383, -0.1059) X_3970 = com[INVERSE(n(INCENTRAL TRIANGLE))] (0.6185, 0.2892) A B C X1 X6 X65 X1018 X55 X1759 X758 X1334 X321 X1930 X79 X2795 X3970 (a, b, c) = (5, 6, 7) | AB = 1

X3970 (X1334com[INVERSE(n(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 \(f(a,b,c) = a(b + c)(b^{2} + c^{2} - bc - ca - ab)\)
Search Value (6, 9, 13): \(-0.031426718635\)
▸ Incident Central Lines16 lines

{1, 6}, {35, 3509}, {39, 3726}, {55, 1759}, {65, 1018}, {79, 2795}, {321, 1930}, {758, 1334}, {942, 3693}, {1500, 3721}, {2170, 3244}, {2171, 3671}, {2276, 3670}, {2294, 2321}, {3216, 3290}, {3496, 3746}