X3711

X3306com(EXTOUCH TRIANGLE)

X3711 = excentral-to-ABC barycentric image of X3306
< 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) { 8, 11 }: Central Line L(8, 11) { 9, 55 }: Central Line L(9, 55) { 214, 956 }: Central Line L(214, 956) { 612, 1100 }: Central Line L(612, 1100) { 45, 2177 }: Central Line L(45, 2177) { 762, 2271 }: Central Line L(762, 2271) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_8 = NAGEL POINT (0.4694, 0.1333) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_956 = INTERSECTION OF LINES X(1)X(6) AND X(3)X(8) (0.4790, 0.1235) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_45 = -BETH CONJUGATE OF X(1) (0.5418, 0.1981) X_2177 = -ISOCONJUGATE OF X(89) (0.5755, 0.2311) X_762 = TRILINEAR CUBE OF X(37) (0.5240, 0.1822) X_2271 = -ISOCONJUGATE OF X(969) (0.5872, 0.2461) X_3711 = com(EXTOUCH TRIANGLE) (0.4744, 0.1320) A B C X8 X11 X9 X55 X214 X956 X612 X1100 X45 X2177 X762 X2271 X3711 (a, b, c) = (5, 6, 7) | AB = 1

X3711 (X3306com(EXTOUCH 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 \(f(a,b,c) = a(b + c - a)(2b + 2c - a)\)
Search Value (6, 9, 13): \(4.294897323134\)
▸ Incident Central Lines12 lines

{8, 11}, {9, 55}, {45, 2177}, {214, 956}, {220, 3119}, {518, 3306}, {612, 1100}, {762, 2271}, {899, 3242}, {936, 3304}, {975, 2334}, {1376, 3218}

▸ Functional Relations2 relations