X1818

INVERSE MIMOSA TRANSFORM OF X1282

X1818 = crosspoint of X3 and X295
< 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) { 3, 48 }: Central Line L(3, 48) { 69, 73 }: Central Line L(69, 73) { 1, 142 }: Central Line L(1, 142) { 212, 394 }: Central Line L(212, 394) { 241, 518 }: Central Line L(241, 518) { 42, 750 }: Central Line L(42, 750) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_48 = CROSSPOINT OF X(1) AND X(63) (0.5412, 0.1246) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_73 = CROSSPOINT OF INCENTER AND CIRCUMCENTER (0.5487, 0.1428) X_1 = INCENTER (0.5714, 0.2333) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_212 = -CEVA CONJUGATE OF X(41) (0.4719, 0.0786) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_241 = -LINE CONJUGATE OF X(55) (1.1217, 1.2442) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_750 = INTERSECTION OF LINES X(1)X(88) AND X(2)X(31) (0.5675, 0.2354) X_1818 = INVERSE MIMOSA TRANSFORM OF X(1282) (-0.1296, -0.2419) A B C X3 X48 X69 X73 X1 X142 X212 X394 X241 X518 X42 X750 X1818 (a, b, c) = (5, 6, 7) | AB = 1

X1818 (INVERSE MIMOSA TRANSFORM OF X1282) 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 \(f(a,b,c) = (\cos A)/(y + z)\),\(x : y : z\) = X1282
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.703893655051\)
▸ Incident Central Lines15 lines

{1, 142}, {3, 48}, {9, 991}, {42, 750}, {69, 73}, {198, 1350}, {212, 394}, {222, 1260}, {241, 518}, {386, 1449}, {521, 656}, {581, 936}, {603, 1259}, {997, 1064}, {1193, 1386}

▸ Functional Relations4 relations