X3976

X978com(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) { 8, 244 }: Central Line L(8, 244) { 518, 978 }: Central Line L(518, 978) { 749, 984 }: Central Line L(749, 984) { 1046, 1191 }: Central Line L(1046, 1191) { 256, 3296 }: Central Line L(256, 3296) 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_8 = NAGEL POINT (0.4694, 0.1333) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_749 = ISOGONAL CONJUGATE OF X(748) (0.6307, 0.4253) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_1191 = 2nd SARAGOSSA POINT OF X(56) (0.6211, 0.2922) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_3296 = ISOGONAL CONJUGATE OF X(3295) (0.5834, 0.2585) X_3976 = com(INTOUCH TRIANGLE) (0.5157, 0.1309) A B C X1 X3 X8 X244 X518 X978 X749 X984 X1046 X1191 X256 X3296 X3976 (a, b, c) = (5, 6, 7) | AB = 1

X3976 (X978com(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 \(f(a,b,c) = a(b^{3} + c^{3} + ab^{2} + ac^{2} - 3abc)\)
Search Value (6, 9, 13): \(2.891973261018\)
▸ Incident Central Lines15 lines

{1, 3}, {8, 244}, {38, 3616}, {43, 3555}, {256, 3296}, {518, 978}, {749, 984}, {1015, 3061}, {1046, 1191}, {1329, 3756}, {1393, 3476}, {1739, 3632}, {2275, 3726}, {2292, 3622}, {2975, 3315}