X3764

X869com[T(bc, b²)]

X3764 = isogonal conjugate of isotomic conjugate of X25760
< 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) { 75, 256 }: Central Line L(75, 256) { 6, 560 }: Central Line L(6, 560) { 291, 751 }: Central Line L(291, 751) { 320, 982 }: Central Line L(320, 982) { 674, 869 }: Central Line L(674, 869) { 42, 2183 }: Central Line L(42, 2183) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_256 = 1st SHARYGIN POINT (0.5601, 0.2146) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_560 = 4th POWER POINT (0.6520, 0.3639) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_751 = ISOGONAL CONJUGATE OF X(750) (0.5754, 0.2311) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_674 = CROSSDIFFERENCE OF X(6) AND X(514) (0.2078, -0.2856) X_869 = INTERSECTION OF LINES X(1)X(2) AND X(31)X(32) (0.6039, 0.2651) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_2183 = -ISOCONJUGATE OF X(104) (1.5000, 2.4495) X_3764 = com[T(bc, b2)] (0.5796, 0.2293) A B C X75 X256 X6 X560 X291 X751 X320 X982 X674 X869 X42 X2183 X3764 (a, b, c) = (5, 6, 7) | AB = 1

X3764 (X869com[T(bc, b²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(a^{2}(b^{3} + c^{3} + abc) : b^{2}(c^{3} + a^{3} + abc) : c^{2}(a^{3} + b^{3} + abc)\)
Search Value (6, 9, 13): \(1.557996022400\)
▸ Incident Central Lines15 lines

{1, 3122}, {2, 2228}, {6, 560}, {31, 2245}, {39, 3271}, {42, 2183}, {75, 256}, {291, 751}, {320, 982}, {511, 2274}, {573, 1918}, {674, 869}, {1837, 2310}, {1964, 2277}, {2275, 3248}

▸ Functional Relations1 relation

  • X3764 = isogonal conjugate of isotomic conjugate of X25760