X3554

INTERSECTION OF LINES X1X_6 AND X19X_604

X3554 = crosspoint of X1 and X1422
< 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, 6 }: Incenter–Symmedian Line { 34, 393 }: Central Line L(34, 393) { 198, 319 }: Central Line L(198, 319) { 239, 326 }: Central Line L(239, 326) { 19, 604 }: Central Line L(19, 604) { 216, 1038 }: Central Line L(216, 1038) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_1422 = -BETH CONJUGATE OF X(189) (0.6044, 0.6471) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_393 = -CROSS CONJUGATE OF X(4) (0.6247, 0.5263) X_198 = -CEVA CONJUGATE OF X(6) (0.4741, -0.0381) X_319 = ISOTOMIC CONJUGATE OF X(79) (0.4549, 0.1161) X_239 = -LINE CONJUGATE OF X(42) (4.2109, 3.7992) X_326 = ISOTOMIC CONJUGATE OF X(158) (0.3354, 0.0219) X_19 = CLAWSON POINT (0.6246, 0.4244) X_604 = -CEVA CONJUGATE OF X(31) (0.6442, 0.3744) X_216 = -CEVA CONJUGATE OF X(51) (0.5201, 0.1353) X_1038 = INTERSECTION OF LINES X(1)X(3) AND X(2)X(34) (0.5104, 0.1211) X_3554 = INTERSECTION OF LINES X(1)X(6) AND X(19)X(604) (0.6589, 0.3371) A B C X1 X1422 X6 X34 X393 X198 X319 X239 X326 X19 X604 X216 X1038 X3554 (a, b, c) = (5, 6, 7) | AB = 1

X3554 (INTERSECTION OF LINES X1X_6 AND X19X_604) 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 \(f(A,B,C) = \sin A - \sin A \sin B \sin C\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(0.676064632589\)
▸ Alternate Coordinates2 forms

  • Trilinears: \(aR - rs : bR - rs : cR - rs\)

  • Trilinears: \(a^{2}bc - S^{2} : b^{2}ca - S^{2} : c^{2}ab - S^{2}\)

▸ Incident Central Lines27 lines

{1, 6}, {19, 604}, {33, 3087}, {34, 393}, {36, 1609}, {48, 2082}, {56, 2262}, {57, 2164}, {198, 319}, {216, 1038}, {239, 326}, {269, 1086}, {282, 1146}, {374, 1696}, {380, 2278}, {577, 1040}, {800, 1015}, {836, 3086}, {1033, 1398}, {1182, 2260}, {1249, 1870}, {1404, 2261}, {1407, 1422}, {1420, 2178}, {1953, 2285}, {3068, 3083}, {3069, 3084}

▸ Functional Relations3 relations