X1834

ZOSMA TRANSFORM OF X28

X1834 = complement of X1043
< A B C >: Reference Triangle △ABC < M_a M_b M_c >: Medial Triangle △M_a M_b M_c [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 1043 }: Central Line L(2, 1043) { 4, 6 }: Van Aubel Line { 10, 37 }: Central Line L(10, 37) { 12, 42 }: Central Line L(12, 42) { 30, 58 }: Central Line L(30, 58) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) M_a = Midpoint M_a of BC (0.8061, 0.2999) M_b = Midpoint M_b of CA (0.3061, 0.2999) M_c = Midpoint M_c of AB (0.5000, 0.0000) X_2 = CENTROID (0.5374, 0.2000) X_1043 = CEVAPOINT OF X(1) AND X(20) (0.4149, 0.0930) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_1834 = ZOSMA TRANSFORM OF X(28) (0.5987, 0.2534) A B C Ma Mb Mc X2 X1043 X4 X6 X10 X37 X12 X42 X30 X58 X1834 (a, b, c) = (5, 6, 7) | AB = 1

X1834 (ZOSMA TRANSFORM OF X28) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: (y + z) sec A : (z + x) sec B : (x + y) sec C,\(x : y : z\) = X28
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X28
Search Value (6, 9, 13): \(1.270516316335\)
▸ Incident Central Lines22 lines

{1, 442}, {2, 1043}, {4, 6}, {5, 386}, {8, 1211}, {10, 37}, {11, 1193}, {12, 42}, {30, 58}, {33, 429}, {43, 1329}, {56, 851}, {65, 225}, {115, 118}, {377, 940}, {405, 1714}, {440, 950}, {496, 995}, {497, 1191}, {524, 1330}, {942, 1086}, {1058, 1616}

▸ Functional Relations5 relations