X3186

X25-CEVA CONJUGATE OF X4

X3186 = X25-Ceva conjugate of X4
< 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) { 4, 69 }: Central Line L(4, 69) { 1, 242 }: Central Line L(1, 242) { 25, 385 }: Central Line L(25, 385) { 6, 419 }: Central Line L(6, 419) { 232, 800 }: Central Line L(232, 800) { 393, 694 }: Central Line L(393, 694) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_4 = ORTHOCENTER (0.6122, 0.3958) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_1 = INCENTER (0.5714, 0.2333) X_242 = -LINE CONJUGATE OF X(71) (0.7507, 0.7161) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_419 = -HIRST INVERSE OF X(25) (0.7266, 0.6950) X_232 = -CEVA CONJUGATE OF X(132) (0.6919, 0.7779) X_800 = CROSSPOINT OF X(2) AND X(64) (0.6501, 0.3499) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_3186 = -CEVA CONJUGATE OF X(4) (0.6627, 0.4791) A B C X25 X4 X69 X1 X242 X385 X6 X419 X232 X800 X393 X694 X3186 (a, b, c) = (5, 6, 7) | AB = 1

X3186 (X25-CEVA CONJUGATE OF X4) 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 \(f(a,b,c) = bc(b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})/(b^{2} + c^{2} - a^{2})\) (M. Iliev, 5/13/07)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.661612451167\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (a^{2}b^{2} + a^{2}c^{2} - b^{2}c^{2})/(b^{2} + c^{2} - a^{2}) (E\). Danneels)

▸ Incident Central Lines16 lines

{1, 242}, {2, 3505}, {4, 69}, {6, 419}, {19, 2319}, {24, 1075}, {25, 385}, {141, 5117}, {232, 800}, {237, 3164}, {393, 694}, {427, 3314}, {571, 1632}, {648, 1974}, {1714, 3144}, {3462, 3542}

▸ Functional Relations6 relations