X3774

X39com[INVERSE(nT(bc, b²))]

< 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) { 10, 37 }: Central Line L(10, 37) { 39, 518 }: Central Line L(39, 518) { 213, 872 }: Central Line L(213, 872) { 100, 1908 }: Central Line L(100, 1908) { 192, 1921 }: Central Line L(192, 1921) { 42, 3121 }: Central Line L(42, 3121) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_213 = -CEVA CONJUGATE OF X(42) (0.6135, 0.2833) X_872 = INTERSECTION OF LINES X(37)X(42) AND X(43)X(75) (0.6029, 0.2656) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_1908 = MIDPOINT OF PU(8) (0.5880, 0.2495) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_1921 = CROSSDIFFERENCE OF PU(12) (-1.0027, -0.8795) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_3121 = DANNEELS PERSPECTOR FOR X(37) (0.8041, 0.1436) X_3774 = com[INVERSE(nT(bc, b2))] (0.5921, 0.2475) A B C X10 X37 X39 X518 X213 X872 X100 X1908 X192 X1921 X42 X3121 X3774 (a, b, c) = (5, 6, 7) | AB = 1

X3774 (X39com[INVERSE(nT(bc, b²))]) 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 \(f(a,b,c) = a^{3}(b + c)(b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(1.217504449691\)
▸ Incident Central Lines9 lines

{10, 37}, {39, 518}, {42, 3121}, {100, 1908}, {192, 1921}, {213, 872}, {984, 2276}, {1045, 3508}, {1574, 3739}