X3123

DANNEELS PERSPECTOR FOR X43

X3123 = crosspoint of X75 and X513
< 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) { 11, 244 }: Central Line L(11, 244) { 38, 1227 }: Central Line L(38, 1227) { 31, 1633 }: Central Line L(31, 1633) { 661, 1084 }: Central Line L(661, 1084) { 350, 2227 }: Central Line L(350, 2227) { 536, 2228 }: Central Line L(536, 2228) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_38 = CROSSPOINT OF X(1) AND X(75) (0.5443, 0.1976) X_1227 = ISOTOMIC CONJUGATE OF X(1168) (0.2551, 0.2499) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_1633 = TCC-PERSPECTOR OF X(651) (0.2619, 0.5832) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_1084 = CROSSPOINT OF X(2) AND X(512) (0.8090, 0.1525) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_2227 = -ISOCONJUGATE OF X(699) (2.8719, 1.7027) X_536 = DIRECTION OF VECTOR AX + BX + CX, where X = X(37) (0.0840, -0.1727) X_2228 = -ISOCONJUGATE OF X(713) (2.7741, 1.7559) X_3123 = DANNEELS PERSPECTOR FOR X(43) (0.8179, 0.1482) A B C X11 X244 X38 X1227 X31 X1633 X661 X1084 X350 X2227 X536 X2228 X3123 (a, b, c) = (5, 6, 7) | AB = 1

X3123 (DANNEELS PERSPECTOR FOR X43) 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 \(f(a,b,c) = (bc - ab - ac)(b - c)^{2}\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.192686567999\)
▸ Incident Central Lines7 lines

{11, 244}, {31, 1633}, {38, 1227}, {350, 2227}, {536, 2228}, {661, 1084}, {1423, 2209}

▸ Functional Relations5 relations