X1317

REFLECTION OF X11 IN X1

X1317 is the antipode of X11 on the incircle.
< 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, 1 }: Feuerbach Line { 1, 5 }: Feuerbach Line { 56, 100 }: Central Line L(56, 100) { 55, 104 }: Central Line L(55, 104) { 7, 528 }: Central Line L(7, 528) 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_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_7 = GERGONNE POINT (0.5903, 0.2769) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) A B C X11 X1 X5 X56 X100 X55 X104 X7 X528 X1317 (a, b, c) = (5, 6, 7) | AB = 1

X1317 (REFLECTION OF X11 IN X1) 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 \(f(a,b,c) = bc(c + a - b)(a + b - c)(b + c - 2a)^{2}\)
Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = (c + a - b)(a + b - c)(b + c - 2a)^{2}\)
Search Value (6, 9, 13): \(0.737481897669\)
▸ Incident Central Lines7 lines

{1, 5}, {7, 528}, {55, 104}, {56, 100}, {149, 388}, {153, 497}, {214, 519}

▸ Functional Relations9 relations