X3862

PERSPECTOR OF ABC AND T(bc, b²)

{X694,X1581}-harmonic conjugate of X3863
< 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) { 694, 1581 }: Central Line L(694, 1581) { 75, 141 }: Central Line L(75, 141) { 37, 256 }: Central Line L(37, 256) { 6, 292 }: Central Line L(6, 292) { 291, 518 }: Central Line L(291, 518) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3863 = PERSPECTOR OF ABC AND T(-bc, b2) (0.5731, 0.2095) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_1581 = ISOGONAL CONJUGATE OF X(1580) (1.0304, 0.0330) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_292 = -HIRST INVERSE OF X(291) (1.0127, 0.0417) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_3862 = PERSPECTOR OF ABC AND T(bc, b2) (1.0241, 0.0354) A B C X3863 X694 X1581 X75 X141 X37 X256 X6 X292 X291 X518 X3862 (a, b, c) = (5, 6, 7) | AB = 1

X3862 (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): \(-0.166464882415\)
▸ Incident Central Lines10 lines

{6, 292}, {37, 256}, {75, 141}, {291, 518}, {660, 2235}, {753, 813}, {984, 3094}, {1333, 2311}, {1755, 2076}, {2276, 3116}