X3781

X9com[INVERSE(nT(bc, c²))]

< 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) { 3, 48 }: Central Line L(3, 48) { 69, 72 }: Central Line L(69, 72) { 63, 295 }: Central Line L(63, 295) { 9, 511 }: Central Line L(9, 511) { 209, 940 }: Central Line L(209, 940) { 220, 1350 }: Central Line L(220, 1350) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_9 = MITTENPUNKT (0.5110, 0.1615) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_209 = -CEVA CONJUGATE OF X(37) (0.7303, 0.4592) X_940 = POINT ALDEBARAN (0.5757, 0.2411) X_220 = -CEVA CONJUGATE OF X(55) (0.4826, 0.1278) X_1350 = REFLECTION OF X(6) IN X(3) (0.4000, -0.0631) X_3781 = com[INVERSE(nT(bc, c2))] (0.4626, 0.0816) A B C X3 X48 X69 X72 X63 X295 X9 X511 X209 X940 X220 X1350 X3781 (a, b, c) = (5, 6, 7) | AB = 1

X3781 (X9com[INVERSE(nT(bc, c²))]) 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 \(f(a,b,c) = a^{2}(b^{2} + c^{2} - a^{2})(b^{2} + c^{2} + bc)\)
Search Value (6, 9, 13): \(5.352098440402\)
▸ Incident Central Lines22 lines

{1, 3688}, {3, 48}, {9, 511}, {35, 2175}, {51, 3305}, {58, 2273}, {63, 295}, {69, 72}, {182, 2323}, {200, 3033}, {209, 940}, {220, 1350}, {238, 3056}, {386, 2300}, {517, 2550}, {674, 1001}, {936, 970}, {984, 1469}, {991, 3730}, {2276, 3736}, {2979, 3219}, {3098, 3220}