X1621

TCC-PERSPECTOR OF X81

X1621 is the tcc-perspector of X81.
< 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) { 2, 11 }: Central Line L(2, 11) { 1, 21 }: Central Line L(1, 21) { 37, 82 }: Central Line L(37, 82) { 42, 238 }: Central Line L(42, 238) { 8, 405 }: Central Line L(8, 405) { 35, 404 }: Central Line L(35, 404) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_82 = ISOGONAL CONJUGATE OF X(38) (0.5943, 0.2703) X_42 = CROSSPOINT OF INCENTER AND SYMMEDIAN POINT (0.5880, 0.2495) X_238 = -LINE CONJUGATE OF X(37) (1.6190, 1.4775) X_8 = NAGEL POINT (0.4694, 0.1333) X_405 = EULER LINE INTERCEPT OF LINE X(1)X(6) (0.5325, 0.1870) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_404 = {X(2),X(3)}-HARMONIC CONJUGATE OF X(21) (0.5538, 0.2429) X_1621 = TCC-PERSPECTOR OF X(81) (0.5431, 0.1961) A B C X2 X11 X1 X21 X37 X82 X42 X238 X8 X405 X35 X404 X1621 (a, b, c) = (5, 6, 7) | AB = 1

X1621 (TCC-PERSPECTOR OF X81) 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 \(f(a,b,c) = a^{2} - bc - ca - ab\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(2.632114869557\)
▸ Linear Combinations1 combination
▸ Incident Central Lines23 lines

{1, 21}, {2, 11}, {3, 962}, {7, 1617}, {8, 405}, {9, 1174}, {22, 1486}, {35, 404}, {36, 551}, {37, 82}, {42, 238}, {43, 748}, {99, 873}, {145, 958}, {171, 902}, {213, 1206}, {226, 1005}, {278, 1013}, {329, 954}, {411, 946}, {517, 1006}, {739, 932}, {985, 1255}

▸ Functional Relations6 relations