X1770

MIMOSA TRANSFORM OF X943

X1770 = cevapoint of X46 and X1717
< 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, 7 }: Soddy Line { 4, 46 }: Central Line L(4, 46) { 30, 65 }: Central Line L(30, 65) { 35, 79 }: Central Line L(35, 79) { 10, 191 }: Central Line L(10, 191) { 109, 225 }: Central Line L(109, 225) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_1717 = MIMOSA TRANSFORM OF X(35) (0.6295, 0.3852) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_4 = ORTHOCENTER (0.6122, 0.3958) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_79 = ISOGONAL CONJUGATE OF X(35) (0.5976, 0.3019) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_109 = Ψ(INCENTER, CIRCUMCENTER) (0.3636, 0.5938) X_225 = -CEVA CONJUGATE OF X(65) (0.6246, 0.4451) X_1770 = MIMOSA TRANSFORM OF X(943) (0.6554, 0.4275) A B C X46 X1717 X1 X7 X4 X30 X65 X35 X79 X10 X191 X109 X225 X1770 (a, b, c) = (5, 6, 7) | AB = 1

X1770 (MIMOSA TRANSFORM OF X943) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = - (\cos A)/x + (\cos B)/y + (\cos C)/z\),\(x : y : z\) = X943
Search Value (6, 9, 13): \(-2.309927773133\)
▸ Incident Central Lines22 lines

{1, 7}, {3, 1836}, {4, 46}, {5, 1155}, {10, 191}, {27, 1780}, {28, 1633}, {30, 65}, {35, 79}, {36, 946}, {40, 1478}, {47, 1754}, {57, 1479}, {109, 225}, {165, 498}, {382, 1837}, {1707, 1714}, {1710, 1782}, {1724, 1738}, {1744, 1826}, {1771, 1785}, {1885, 1905}

▸ Functional Relations1 relation

Notes

Let IaIbIc be the reflection triangle of X1. Let A' be the cevapoint of Ib and Ic, and define B' and C' cyclically. The lines AA', BB', CC' concur in X1770. (Randy Hutson, July 20, 2016)