X3672

X1449com(INTOUCH TRIANGLE)

X3672 = anticomplement of X2345
< 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, 7 }: Soddy Line { 2, 37 }: Central Line L(2, 37) { 6, 144 }: Central Line L(6, 144) { 69, 145 }: Central Line L(69, 145) { 239, 391 }: Central Line L(239, 391) { 307, 938 }: Central Line L(307, 938) 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_1219 = ISOGONAL CONJUGATE OF X(1191) (0.5037, 0.1756) X_7 = GERGONNE POINT (0.5903, 0.2769) X_2 = CENTROID (0.5374, 0.2000) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_144 = ANTICOMPLEMENT OF X(7) (0.4317, 0.0461) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_391 = INTERSECTION OF LINES X(2,6) AND X(8,9) (0.4857, 0.1443) X_307 = ISOTOMIC CONJUGATE OF X(29) (0.4659, 0.0959) X_938 = ANTICOMPLEMENT OF X(936) (0.5846, 0.2462) X_3672 = com(INTOUCH TRIANGLE) (0.5678, 0.2250) A B C X1 X1219 X7 X2 X37 X6 X144 X69 X145 X239 X391 X307 X938 X3672 (a, b, c) = (5, 6, 7) | AB = 1

X3672 (X1449com(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 \(f(a,b,c) = a^{2} + b^{2} + c^{2} + 2ab + 2ca - 2bc\)
Search Value (6, 9, 13): \(1.838231279705\)
▸ Incident Central Lines20 lines

{1, 7}, {2, 37}, {6, 144}, {55, 3598}, {63, 2257}, {69, 145}, {81, 2255}, {86, 3445}, {142, 3247}, {190, 3618}, {239, 391}, {307, 938}, {319, 3621}, {320, 3623}, {527, 1449}, {941, 2481}, {999, 1014}, {1266, 3616}, {1423, 2269}, {1429, 2268}

▸ Functional Relations3 relations