X3422

X1-VERTEX CONJUGATE OF X19

X3422 = isogonal conjugate of X1478
< 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, 24 }: Central Line L(1, 24) { 3, 47 }: Central Line L(3, 47) { 35, 78 }: Central Line L(35, 78) { 36, 77 }: Central Line L(36, 77) { 29, 1479 }: Central Line L(29, 1479) { 55, 1807 }: Central Line L(55, 1807) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1064 = INTERSECTION OF LINES X(1)X(4) AND X(3)X(31) (0.5648, 0.2070) X_1 = INCENTER (0.5714, 0.2333) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_47 = -BETH CONJUGATE OF X(34) (0.7279, 0.4389) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_78 = ISOGONAL CONJUGATE OF X(34) (0.3835, 0.0491) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_77 = ISOGONAL CONJUGATE OF X(33) (0.5270, 0.1305) X_29 = CEVAPOINT OF INCENTER AND ORTHOCENTER (0.5903, 0.3384) X_1479 = {X(1),X(4)}-HARMONIC CONJUGATE OF X(1478) (0.5371, 0.0965) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1807 = INVERSE MIMOSA TRANSFORM OF X(484) (0.8312, -0.0318) X_3422 = -VERTEX CONJUGATE OF X(19) (0.5568, 0.1860) A B C X1064 X1 X24 X3 X47 X35 X78 X36 X77 X29 X1479 X55 X1807 X3422 (a, b, c) = (5, 6, 7) | AB = 1

X3422 (X1-VERTEX CONJUGATE OF X19) 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 \(f(a,b,c) = a/[a^{2}vwyz - ux(bw + cv)(bz + cy)]\), where \(u : v : w\) = X1 and \(x : y : z\) = X19
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.898283102852\)
▸ Alternate Coordinates1 form

  • Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a^{2}/[a^{4} + 2a^{2}bc - (b^{2} - c^{2})^{2}] (E\). Danneels)

▸ Incident Central Lines11 lines

{1, 24}, {3, 47}, {29, 1479}, {35, 78}, {36, 77}, {55, 1807}, {219, 2174}, {573, 2359}, {1065, 1478}, {2163, 2291}, {2301, 2338}

▸ Functional Relations2 relations