X1999

ORTHOCORRESPONDENT OF X10

X1999 = X65-Ceva conjugate of X894
< 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, 2 }: Nagel Line { 63, 192 }: Central Line L(63, 192) { 6, 312 }: Central Line L(6, 312) { 27, 295 }: Central Line L(27, 295) { 37, 333 }: Central Line L(37, 333) { 81, 314 }: Central Line L(81, 314) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_894 = ISOGONAL CONJUGATE OF X(893) (0.5501, 0.2184) X_1 = INCENTER (0.5714, 0.2333) X_2 = CENTROID (0.5374, 0.2000) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_192 = -CEVA CONJUGATE OF X(2) (CONGRUENT PARALLELIANS POINT) (0.6147, 0.2635) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_312 = ISOTOMIC CONJUGATE OF X(57) (0.4256, 0.1081) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_295 = ISOGONAL CONJUGATE OF X(242) (1.0582, 0.0142) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_81 = CEVAPOINT OF INCENTER AND SYMMEDIAN POINT (0.5849, 0.2510) X_314 = ISOTOMIC CONJUGATE OF X(65) (0.4457, 0.1206) X_1999 = ORTHOCORRESPONDENT OF X(10) (0.6884, 0.3479) A B C X65 X894 X1 X2 X63 X192 X6 X312 X27 X295 X37 X333 X81 X314 X1999 (a, b, c) = (5, 6, 7) | AB = 1

X1999 (ORTHOCORRESPONDENT OF X10) 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 \(x : y : z\) = X10
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.298651659705\)
▸ Alternate Coordinates1 form

  • Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = bc(a^{3} + a^{2}b + a^{2}c + abc - b^{2}c - bc^{2})\) (M. Iliev, 5/13/07)

▸ Incident Central Lines15 lines

{1, 2}, {6, 312}, {27, 295}, {37, 333}, {63, 192}, {75, 940}, {81, 314}, {100, 1402}, {171, 740}, {193, 329}, {226, 1943}, {319, 1211}, {350, 1965}, {553, 1266}, {664, 1427}

▸ Functional Relations2 relations