X1890

ZOSMA TRANSFORM OF X984

X1890 = X29-beth conjugate of X1826
< 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, 9 }: Orthocenter–Spieker Line { 7, 34 }: Central Line L(7, 34) { 28, 142 }: Central Line L(28, 142) { 27, 162 }: Central Line L(27, 162) { 82, 225 }: Central Line L(82, 225) { 33, 390 }: Central Line L(33, 390) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1826 = ZOSMA TRANSFORM OF X(6) (0.6052, 0.3795) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_7 = GERGONNE POINT (0.5903, 0.2769) X_34 = -BETH CONJUGATE OF X(4) (0.6332, 0.4792) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_27 = CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER (0.6182, 0.4112) X_162 = CEVAPOINT OF X(108) AND X(109) (0.4897, 0.6018) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_390 = REFLECTION OF GERGONNE POINT IN INCENTER (0.5526, 0.1897) X_1890 = ZOSMA TRANSFORM OF X(984) (0.6186, 0.4105) A B C X29 X1826 X4 X9 X7 X34 X28 X142 X27 X162 X82 X225 X33 X390 X1890 (a, b, c) = (5, 6, 7) | AB = 1

X1890 (ZOSMA TRANSFORM OF X984) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((y + z) \sec A : (z + x) \sec B : (x + y) \sec C\), where \(x : y : z\) = X984
Search Value (6, 9, 13): \(-2.770720004903\)
▸ Incident Central Lines13 lines

{4, 9}, {7, 34}, {25, 1001}, {27, 162}, {28, 142}, {33, 390}, {82, 225}, {428, 528}, {518, 1829}, {751, 1877}, {1445, 1452}, {1724, 1738}, {1737, 1747}

▸ Functional Relations2 relations