X1768

MIMOSA TRANSFORM OF X521

X1768 = trilinear pole wrt excentral triangle of line X4X9
< 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, 57 }: Central Line L(11, 57) { 1, 104 }: Central Line L(1, 104) { 46, 80 }: Central Line L(46, 80) { 10, 153 }: Central Line L(10, 153) { 63, 100 }: Central Line L(63, 100) { 3, 191 }: Central Line L(3, 191) 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_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1 = INCENTER (0.5714, 0.2333) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_1768 = MIMOSA TRANSFORM OF X(521) (1.1429, -0.7582) A B C X11 X57 X1 X104 X46 X80 X10 X153 X63 X100 X3 X191 X1768 (a, b, c) = (5, 6, 7) | AB = 1

X1768 (MIMOSA TRANSFORM OF X521) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a^{5} - a^{4} (b + c) - a^{3} (2 b^{2} - 5 b c + 2 c^{2}) + 2 a^{2} (b - c)^{2} (b + c) + a (b - c)^{2} (b^{2} - b c + c^{2}) - b^{5} + b^{4} c + b c^{4} - c^{5} : :\)
Search Value (6, 9, 13): \(20.235470797377\)

X1768 lies on the Bevan circle, the excentral-hexyl ellipse.

▸ Incident Central Lines16 lines

{1, 104}, {3, 191}, {10, 153}, {11, 57}, {36, 1727}, {40, 550}, {46, 80}, {63, 100}, {119, 1698}, {149, 516}, {484, 515}, {971, 1155}, {1156, 1445}, {1317, 1697}, {1708, 1750}, {1765, 1781}

▸ Functional Relations8 relations