X1854

ZOSMA TRANSFORM OF X208

X1854 = reflection of X221 in 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) { 221, 1 }: Central Line L(221, 1) { 1, 84 }: Central Line L(1, 84) { 33, 64 }: Central Line L(33, 64) { 56, 774 }: Central Line L(56, 774) { 55, 976 }: Central Line L(55, 976) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_1 = INCENTER (0.5714, 0.2333) X_84 = ISOGONAL CONJUGATE OF X(40) (0.6071, 0.6816) X_33 = PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES (0.6019, 0.3546) X_64 = ISOGONAL CONJUGATE OF X(20) (0.5579, 1.5943) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_774 = CROSSPOINT OF X(1) AND X(158) (0.6363, 0.3186) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_976 = INTERSECTION OF LINES X(1)X(2) AND X(3)X(38) (0.5520, 0.2143) X_1854 = ZOSMA TRANSFORM OF X(208) (0.5955, 0.5353) A B C X221 X1 X84 X33 X64 X56 X774 X55 X976 X1854 (a, b, c) = (5, 6, 7) | AB = 1

X1854 (ZOSMA TRANSFORM OF X208) 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 \(x : y : z\) = X208
Barycentrics: \((y + z) \tan A : (z + x) \tan B : (x + y) \tan C\), where \(x : y : z\) = X208
Search Value (6, 9, 13): \(3.711066237038\)
▸ Alternate Coordinates1 form

  • Trilinears: \((b + c - a)[a^{5} + 2a^{2} (b - c)^{2} (b + c) - a(b^{2} - c^{2})^{2} - 2(b - c)^{2} (b + c) (b^{2} + c^{2})] : :\)

▸ Incident Central Lines10 lines

{1, 84}, {6, 1858}, {33, 64}, {55, 976}, {56, 774}, {154, 968}, {227, 1490}, {960, 1040}, {1192, 1452}, {1837, 1853}

▸ Functional Relations3 relations