X985

ISOGONAL CONJUGATE OF X984

X985 is the isogonal conjugate of X984.
< 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, 32 }: Central Line L(1, 32) { 2, 31 }: Central Line L(2, 31) { 6, 291 }: Central Line L(6, 291) { 58, 274 }: Central Line L(58, 274) { 105, 825 }: Central Line L(105, 825) { 81, 982 }: Central Line L(81, 982) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_984 = MIDPOINT OF X(8) AND X(192) (0.5421, 0.1984) X_1 = INCENTER (0.5714, 0.2333) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_291 = 2nd SHARYGIN POINT (1.0249, 0.0364) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_105 = Λ(INCENTER, SYMMEDIAN POINT) (0.9714, -0.0933) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_982 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(38) (0.5508, 0.1955) X_985 = ISOGONAL CONJUGATE OF X(984) (0.5961, 0.2693) A B C X984 X1 X32 X2 X31 X6 X291 X58 X274 X105 X825 X81 X982 X985 (a, b, c) = (5, 6, 7) | AB = 1

X985 (ISOGONAL CONJUGATE OF X984) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/[b^{2} + bc + c^{2}]\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)
Search Value (6, 9, 13): \(1.038547283600\)
▸ Incident Central Lines8 lines

{1, 32}, {2, 31}, {6, 291}, {58, 274}, {81, 982}, {105, 825}, {279, 1106}, {727, 789}

▸ Functional Relations2 relations