X3784

X57com[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, 73 }: Central Line L(3, 73) { 63, 295 }: Central Line L(63, 295) { 57, 511 }: Central Line L(57, 511) { 1, 1401 }: Central Line L(1, 1401) { 36, 1397 }: Central Line L(36, 1397) { 165, 1362 }: Central Line L(165, 1362) 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_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1 = INCENTER (0.5714, 0.2333) X_1401 = -BETH CONJUGATE OF X(38) (0.6188, 0.3077) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_1397 = -BETH CONJUGATE OF X(31) (0.6524, 0.4026) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1362 = BRISSE TRANSFORM OF X(105) (0.4408, 0.4266) X_3784 = com[INVERSE(nT(-bc, c2))] (0.4741, 0.0804) A B C X3 X73 X63 X295 X57 X511 X1 X1401 X36 X1397 X165 X1362 X3784 (a, b, c) = (5, 6, 7) | AB = 1

X3784 (X57com[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): \(4.627572011614\)
▸ Incident Central Lines16 lines

{1, 1401}, {3, 73}, {36, 1397}, {51, 3306}, {57, 511}, {63, 295}, {165, 1362}, {171, 1469}, {182, 2003}, {200, 2810}, {394, 1473}, {517, 3474}, {982, 3056}, {1040, 1364}, {1350, 1407}, {2979, 3218}