X1844

ZOSMA TRANSFORM OF X79

X1844 = X4-Ceva conjugate of X1838
< 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, 19 }: Central Line L(1, 19) { 33, 46 }: Central Line L(33, 46) { 4, 79 }: Central Line L(4, 79) { 35, 186 }: Central Line L(35, 186) { 29, 758 }: Central Line L(29, 758) { 407, 1785 }: Central Line L(407, 1785) 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_1838 = ZOSMA TRANSFORM OF X(35) (0.6188, 0.4218) X_1 = INCENTER (0.5714, 0.2333) X_19 = CLAWSON POINT (0.6246, 0.4244) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_186 = INVERSE-IN-CIRCUMCIRCLE OF X(4) (0.7957, 0.8758) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_758 = EVEN (1, 3) INFINITY POINT (0.1821, -0.2671) X_407 = CROSSPOINT OF X(4) AND X(225) (0.6211, 0.4189) X_1785 = MIMOSA TRANSFORM OF X(1295) (0.7297, 0.8635) X_1844 = ZOSMA TRANSFORM OF X(79) (0.6067, 0.3599) A B C X4 X1838 X1 X19 X33 X46 X79 X35 X186 X29 X758 X407 X1785 X1844 (a, b, c) = (5, 6, 7) | AB = 1

X1844 (ZOSMA TRANSFORM OF X79) 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 \(x : y : z\) = X79
Barycentrics: \((y + z) \tan A : (z + x) \tan B : (x + y) \tan C\), where \(x : y : z\) = X79
Search Value (6, 9, 13): \(3.019250075338\)
▸ Incident Central Lines11 lines

{1, 19}, {4, 79}, {29, 758}, {33, 46}, {35, 186}, {354, 1871}, {407, 1785}, {942, 1838}, {1828, 1884}, {1831, 1870}, {1846, 1887}

▸ Functional Relations2 relations

Notes

Let HaHbHc be the orthic triangle. Let A″ be the incenter of AHbHc, and define B″ and C″ cyclically. The lines HaA″, HbB″, HcC″ concur in X1844. (Randy Hutson, January 29, 2018)