X3550

INTERSECTION OF LINES X1X_3 AND X31X_43

X3550 = X983-Ceva conjugate of X1
< 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, 3 }: OI Line (Incenter–Circumcenter Line) { 31, 34 }: Central Line L(31, 34) { 2, 902 }: Central Line L(2, 902) { 612, 846 }: Central Line L(612, 846) { 595, 978 }: Central Line L(595, 978) { 238, 1376 }: Central Line L(238, 1376) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_983 = ISOGONAL CONJUGATE OF X(982) (0.5890, 0.2731) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_2 = CENTROID (0.5374, 0.2000) X_902 = CROSSPOINT OF X(6) AND X(106) (1.2500, 1.2247) X_612 = INTERSECTION OF LINES X(1)X(2) AND X(9)X(31) (0.5582, 0.2203) X_846 = 4th SHARYGIN POINT (0.5437, 0.1969) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_978 = -CEVA CONJUGATE OF X(1) (0.7456, 0.4040) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_3550 = INTERSECTION OF LINES X(1)X(3) AND X(31)X(43) (0.6105, 0.3051) A B C X983 X1 X3 X31 X34 X2 X902 X612 X846 X595 X978 X238 X1376 X3550 (a, b, c) = (5, 6, 7) | AB = 1

X3550 (INTERSECTION OF LINES X1X_3 AND X31X_43) 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 \(f(a,b,c) = 2a^{2} + bc - ca - ab\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.765531322671\)
▸ Incident Central Lines23 lines

{1, 3}, {2, 902}, {31, 34}, {32, 2319}, {42, 3097}, {63, 3099}, {81, 2177}, {87, 2209}, {172, 3208}, {200, 1707}, {238, 1376}, {595, 978}, {609, 1018}, {612, 846}, {614, 1054}, {750, 1621}, {968, 1961}, {983, 1423}, {1120, 2163}, {1740, 1918}, {1955, 2947}, {2308, 3240}, {2329, 3053}

▸ Functional Relations3 relations