X2003

ORTHOCORRESPONDENT OF X36

X2003 = X1442-Ceva conjugate of X35
< 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, 57 }: Central Line L(6, 57) { 1, 90 }: Central Line L(1, 90) { 58, 73 }: Central Line L(58, 73) { 42, 109 }: Central Line L(42, 109) { 81, 226 }: Central Line L(81, 226) { 65, 267 }: Central Line L(65, 267) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1442 = -BETH CONJUGATE OF X(319) (0.5612, 0.2097) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_90 = -CROSS CONJUGATE OF X(1) (0.1022, 0.0201) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_226 = -CEVA CONJUGATE OF X(65) (0.5778, 0.2588) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_267 = ISOGONAL CONJUGATE OF X(191) (0.6207, 0.3648) X_2003 = ORTHOCORRESPONDENT OF X(36) (0.5923, 0.2428) A B C X1442 X35 X6 X57 X1 X90 X58 X73 X42 X109 X81 X226 X65 X267 X2003 (a, b, c) = (5, 6, 7) | AB = 1

X2003 (ORTHOCORRESPONDENT OF X36) 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 \(f(a,b,c) = yz + (-x \cos A + y \cos B + z \cos C)x\), where \(x : y : z\) = X36
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.303836241737\)
▸ Alternate Coordinates4 forms

  • Trilinears: \(\sin(3A/2) \sec(A/2) : \sin(3B/2) \sec(B/2) : \sin(3C/2) \sec(C/2)\) (M. Iliev, 4/12/07)

  • Trilinears: \((\sin A + \sin 2A)/(1 + \cos A) : (\sin B + \sin 2B)/(1 + \cos B) : (\sin C + \sin 2C)/(1 + \cos C)\) (M. Iliev, 4/12/07)

  • Trilinears: \((1 + 2 \cos A) \tan(A/2) : (1 + 2 \cos B) \tan(B/2) : (1 + 2 \cos C) \tan(C/2)\) (M. Iliev, 4/12/07)

  • Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a(b^{2} + c^{2} - a^{2} + bc)/(b + c - a)\) (M. Iliev, 5/13/07)

▸ Incident Central Lines22 lines

{1, 90}, {6, 57}, {9, 394}, {35, 500}, {42, 109}, {56, 1203}, {58, 73}, {63, 1993}, {65, 267}, {77, 1708}, {81, 226}, {84, 1181}, {212, 991}, {255, 581}, {323, 1442}, {354, 1421}, {386, 603}, {648, 1947}, {894, 1943}, {1171, 1400}, {1397, 1469}, {1401, 1428}

▸ Functional Relations2 relations