X3864

PERSPECTOR OF ABC AND T(bc, c²)

X3864 is the perspector of ABC and t(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) { 1, 39 }: Central Line L(1, 39) { 10, 257 }: Central Line L(10, 257) { 76, 334 }: Central Line L(76, 334) { 335, 726 }: Central Line L(335, 726) { 761, 813 }: Central Line L(761, 813) { 511, 1757 }: Central Line L(511, 1757) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_334 = ISOTOMIC CONJUGATE OF X(238) (1.0545, 0.0278) X_335 = ISOTOMIC CONJUGATE OF X(239) (1.0387, 0.0318) X_726 = EVEN (- 2, -1) INFINITY POINT (1.0187, 0.5358) X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT (0.9239, -0.1820) X_813 = o-(- 1, 1) CIRCUMCIRCLE POINT (0.9721, -0.0916) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_1757 = MIMOSA TRANSFORM OF X(295) (2.6667, 2.7217) X_3864 = PERSPECTOR OF ABC AND T(bc, c2) (1.0375, 0.0309) A B C X1 X39 X10 X257 X76 X334 X335 X726 X761 X813 X511 X1757 X3864 (a, b, c) = (5, 6, 7) | AB = 1

X3864 (PERSPECTOR OF ABC AND T(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 \(f(a,b,c) = a(b^{2} - ac)(c^{2} - ab)(b^{2} + bc + c^{2})\)
Search Value (6, 9, 13): \(-0.254937696830\)
▸ Incident Central Lines8 lines

{1, 39}, {10, 257}, {76, 334}, {295, 3497}, {335, 726}, {511, 1757}, {761, 813}, {984, 3094}

▸ Functional Relations1 relation