X3689

X3218com(EXTOUCH TRIANGLE)

X3689 = crossdifference of every pair of points on line X57X1022
< 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) { 9, 55 }: Central Line L(9, 55) { 100, 518 }: Central Line L(100, 518) { 44, 678 }: Central Line L(44, 678) { 214, 519 }: Central Line L(214, 519) { 42, 1100 }: Central Line L(42, 1100) { 650, 663 }: Central Line L(650, 663) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_678 = CROSSPOINT OF X(1) AND X(44) (0.3571, 0.3499) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1100 = COMPLEMENT OF X(319) (0.5787, 0.2419) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_3689 = com(EXTOUCH TRIANGLE) (-1.4286, -1.3997) A B C X9 X55 X100 X518 X44 X678 X214 X519 X42 X1100 X650 X663 X3689 (a, b, c) = (5, 6, 7) | AB = 1

X3689 (X3218com(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 \(f(a,b,c) = a(a - b - c)(2a - b - c)\)
Search Value (6, 9, 13): \(9.911756704670\)
▸ Incident Central Lines21 lines

{8, 2320}, {9, 55}, {37, 2177}, {42, 1100}, {44, 678}, {78, 3057}, {100, 518}, {214, 519}, {354, 1376}, {528, 908}, {612, 3290}, {650, 663}, {899, 1279}, {936, 3303}, {1104, 3214}, {1261, 2194}, {1318, 1320}, {1386, 3240}, {1837, 3189}, {2098, 2136}, {3058, 3452}

▸ Functional Relations3 relations