X3863

PERSPECTOR OF ABC AND T(-bc, b²)

X3863 is the perspector of ABC and t(-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) { 37, 256 }: Central Line L(37, 256) { 75, 257 }: Central Line L(75, 257) { 6, 893 }: Central Line L(6, 893) { 1178, 1333 }: Central Line L(1178, 1333) { 904, 1964 }: Central Line L(904, 1964) { 3061, 3094 }: Central Line L(3061, 3094) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_1178 = 1st SARAGOSSA POINT OF X(82) (0.6029, 0.2656) X_1333 = POINT ALULA (0.6308, 0.3181) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_1964 = BICENTRIC SUM OF PU(36) (0.6058, 0.2641) X_3061 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(257) (0.4848, 0.1304) X_3094 = INTERSECTION OF LINES X(2)X(694) AND X(3)X(6) (0.5556, 0.1938) X_3863 = PERSPECTOR OF ABC AND T(-bc, b2) (0.5731, 0.2095) A B C X37 X256 X75 X257 X6 X893 X1178 X1333 X904 X1964 X3061 X3094 X3863 (a, b, c) = (5, 6, 7) | AB = 1

X3863 (PERSPECTOR OF ABC AND T(-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 \(f(a,b,c) = a^{2}(b^{2} + ac)(c^{2} + ab)(b^{2} - bc + c^{2})\)
Search Value (6, 9, 13): \(1.717386422395\)
▸ Incident Central Lines7 lines

{6, 893}, {37, 256}, {75, 257}, {904, 1964}, {1178, 1333}, {3056, 3116}, {3061, 3094}

▸ Functional Relations1 relation