X3865

PERSPECTOR OF ABC AND T(-bc, c²)

X3865 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, 256 }: Central Line L(1, 256) { 10, 257 }: Central Line L(10, 257) { 39, 893 }: Central Line L(39, 893) { 904, 995 }: Central Line L(904, 995) { 986, 3095 }: Central Line L(986, 3095) { 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_1 = INCENTER (0.5714, 0.2333) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_257 = ISOGONAL CONJUGATE OF X(172) (0.5240, 0.1822) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_893 = -CROSS CONJUGATE OF X(292) (0.5910, 0.2480) X_904 = -HIRST INVERSE OF X(256) (0.6163, 0.2816) X_995 = MIDPOINT OF X(1) AND X(43) (0.6036, 0.2648) X_986 = INTERSECTION OF LINES X(1)X(3) AND X(8)X(38) (0.5588, 0.2101) X_3095 = INTERSECTION OF LINES X(3)X(6) AND X(5)X(76) (0.6556, 0.3590) 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_3865 = PERSPECTOR OF ABC AND T(-bc, c2) (0.5380, 0.1781) A B C X1 X256 X10 X257 X39 X893 X904 X995 X986 X3095 X3061 X3094 X3865 (a, b, c) = (5, 6, 7) | AB = 1

X3865 (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): \(2.559050777550\)
▸ Incident Central Lines6 lines

{1, 256}, {10, 257}, {39, 893}, {904, 995}, {986, 3095}, {3061, 3094}

▸ Functional Relations1 relation