X1838

ZOSMA TRANSFORM OF X35

X1838 = X4-Ceva conjugate of X1844
< 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, 4 }: Incenter–Orthocenter Line { 28, 36 }: Central Line L(28, 36) { 19, 46 }: Central Line L(19, 46) { 27, 58 }: Central Line L(27, 58) { 10, 92 }: Central Line L(10, 92) { 11, 133 }: Central Line L(11, 133) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1844 = ZOSMA TRANSFORM OF X(79) (0.6067, 0.3599) X_1 = INCENTER (0.5714, 0.2333) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_19 = CLAWSON POINT (0.6246, 0.4244) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_133 = INTERSECTION OF LINES X(4)X(74) AND X(5)X(122) (0.5928, 0.5014) X_1838 = ZOSMA TRANSFORM OF X(35) (0.6188, 0.4218) A B C X4 X1844 X1 X28 X36 X19 X46 X27 X58 X10 X92 X11 X133 X1838 (a, b, c) = (5, 6, 7) | AB = 1

X1838 (ZOSMA TRANSFORM OF X35) 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,\(x : y : z\) = X35
Barycentrics: (y + z) tan A : (z + x) tan B : (x + y) tan C,\(x : y : z\) = X35
Search Value (6, 9, 13): \(-1.406928158728\)
▸ Incident Central Lines30 lines

{1, 4}, {2, 1076}, {5, 1214}, {10, 92}, {11, 133}, {19, 46}, {20, 1074}, {27, 58}, {28, 36}, {29, 1125}, {30, 1852}, {47, 1754}, {53, 1108}, {57, 1118}, {65, 1243}, {79, 1172}, {158, 273}, {235, 1893}, {281, 1698}, {403, 1873}, {407, 1829}, {412, 516}, {427, 1867}, {442, 1841}, {517, 1888}, {942, 1844}, {1426, 1905}, {1598, 1617}, {1828, 1894}, {1831, 1835}

▸ Functional Relations5 relations