X3254

REFLECTION OF X9 IN X11

X3254 is the reflection of X9 in X11.
< 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) { 9, 11 }: Central Line L(9, 11) { 7, 149 }: Central Line L(7, 149) { 100, 142 }: Central Line L(100, 142) { 1, 528 }: Central Line L(1, 528) { 80, 518 }: Central Line L(80, 518) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_9 = MITTENPUNKT (0.5110, 0.1615) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_7 = GERGONNE POINT (0.5903, 0.2769) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_1 = INCENTER (0.5714, 0.2333) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_518 = ISOGONAL CONJUGATE OF X(105) (0.9154, 0.6489) X_3254 = REFLECTION OF X(9) IN X(11) (0.9584, -0.0282) A B C X9 X11 X7 X149 X100 X142 X1 X528 X80 X518 X3254 (a, b, c) = (5, 6, 7) | AB = 1

X3254 (REFLECTION OF X9 IN X11) 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 \(f(a,b,c) = bc(b + c - a)/(bc - (b + c - a)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.714297543260\)
▸ Incident Central Lines13 lines

{1, 528}, {4, 2801}, {7, 149}, {9, 11}, {80, 518}, {100, 142}, {104, 516}, {294, 2323}, {320, 2481}, {390, 2320}, {527, 1156}, {943, 1125}, {1000, 2550}

▸ Functional Relations4 relations