X3770

X3736com[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) { 6, 76 }: Central Line L(6, 76) { 319, 321 }: Central Line L(319, 321) { 314, 524 }: Central Line L(314, 524) { 256, 714 }: Central Line L(256, 714) { 99, 1030 }: Central Line L(99, 1030) { 313, 894 }: Central Line L(313, 894) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_321 = ISOTOMIC CONJUGATE OF X(81) (0.4800, 0.1527) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_524 = ISOGONAL CONJUGATE OF X(111) (0.1376, -0.2297) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_714 = EVEN (- 3, - 1) INFINITY POINT (1.0302, 0.5186) X_99 = STEINER POINT (0.1109, 0.4322) X_1030 = ISOGONAL CONJUGATE OF X(1029) (0.5271, 0.1468) X_313 = ISOTOMIC CONJUGATE OF X(58) (0.4368, 0.1249) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_3770 = com[T(bc, c2)] (0.4922, 0.1707) A B C X6 X76 X319 X321 X314 X524 X256 X714 X99 X1030 X313 X894 X3770 (a, b, c) = (5, 6, 7) | AB = 1

X3770 (X3736com[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 \(f(a,b,c) = bc(a^{3} + abc + b^{2}c + bc^{2})\)
Search Value (6, 9, 13): \(3.854724391916\)
▸ Incident Central Lines19 lines

{6, 76}, {37, 1655}, {75, 1654}, {81, 1230}, {99, 1030}, {239, 1269}, {256, 714}, {274, 1213}, {310, 2238}, {313, 894}, {314, 524}, {319, 321}, {350, 1100}, {384, 2220}, {385, 1333}, {538, 2092}, {594, 668}, {1228, 2303}, {1330, 3416}