X3670

X3293com(INTOUCH 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) incircle: Incircle of △ABC { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 10, 38 }: Central Line L(10, 38) { 79, 256 }: Central Line L(79, 256) { 191, 238 }: Central Line L(191, 238) { 81, 849 }: Central Line L(81, 849) { 244, 1125 }: Central Line L(244, 1125) 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_10 = SPIEKER CENTER (0.5204, 0.1833) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_849 = 4th HATZIPOLAKIS-YIU POINT (0.6376, 0.3351) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_3670 = com(INTOUCH TRIANGLE) (0.5558, 0.2045) A B C X1 X3 X10 X38 X79 X256 X191 X238 X81 X849 X244 X1125 X3670 (a, b, c) = (5, 6, 7) | AB = 1

X3670 (X3293com(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 \(f(a,b,c) = a(b^{3} + c^{3} + ab^{2} + ac^{2})\)
Search Value (6, 9, 13): \(2.160977892217\)
▸ Incident Central Lines23 lines

{1, 3}, {6, 1759}, {10, 38}, {58, 3218}, {63, 1724}, {72, 3216}, {79, 256}, {81, 849}, {191, 238}, {226, 1393}, {240, 1838}, {244, 1125}, {307, 1210}, {442, 1086}, {518, 3293}, {726, 1089}, {758, 1193}, {975, 3306}, {984, 1698}, {1046, 1203}, {1100, 3285}, {1107, 3125}, {3290, 3294}