X1616

TCC-PERSPECTOR OF X56

X1616 is the tcc-perspector of X56.
< 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, 6 }: Incenter–Symmedian Line { 55, 1201 }: Central Line L(55, 1201) { 42, 1293 }: Central Line L(42, 1293) { 221, 1319 }: Central Line L(221, 1319) { 595, 999 }: Central Line L(595, 999) { 962, 1086 }: Central Line L(962, 1086) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1201 = 3rd SARAGOSSA POINT OF X(56) (0.6184, 0.2793) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_1293 = COLLINGS TRANSFORM OF X(121) (0.0000, 0.2041) X_221 = -CEVA CONJUGATE OF X(56) (0.5474, -0.0688) X_1319 = BEVAN-SCHRÖDER POINT (0.9524, 0.9331) X_595 = 2nd HATZIPOLAKIS-YIU POINT (0.6456, 0.3307) X_999 = MIDPOINT OF X(1) AND X(57) (0.5926, 0.2722) X_962 = LONGUET-HIGGINS POINT (0.7551, 0.6582) X_1086 = CENTER OF HYPERBOLA {{A,B,C,X(2),X(7)|} (0.7687, 0.1000) X_1616 = TCC-PERSPECTOR OF X(56) (0.7600, 0.4572) A B C X1 X6 X55 X1201 X42 X1293 X221 X1319 X595 X999 X962 X1086 X1616 (a, b, c) = (5, 6, 7) | AB = 1

X1616 (TCC-PERSPECTOR OF X56) 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 \(f(a,b,c) = a[(a + b + c)^{2} - 8bc]\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(-0.644465451766\)
▸ Incident Central Lines10 lines

{1, 6}, {42, 1293}, {55, 1201}, {221, 1319}, {595, 999}, {614, 3057}, {902, 1392}, {962, 1086}, {1035, 1457}, {1407, 1420}

▸ Functional Relations4 relations