X2099

REFLECTION OF X55 IN X1

X2099 is the reflection of X55 in X1.
< 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) { 55, 1 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 8, 12 }: Central Line L(8, 12) { 80, 381 }: Central Line L(80, 381) { 145, 388 }: Central Line L(145, 388) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_80 = REFLECTION OF INCENTER IN FEUERBACH POINT (0.8980, -0.1000) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_2099 = REFLECTION OF X(55) IN X(1) (0.5938, 0.2745) A B C X55 X1 X3 X8 X12 X80 X381 X145 X388 X2099 (a, b, c) = (5, 6, 7) | AB = 1

X2099 (REFLECTION OF X55 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 \(f(a,b,c) = (a + b - c)(a - b + c)(a - 2b - 2c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.745147602777\)
▸ Alternate Coordinates1 form

  • Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A,B,C) = 1 - \cos A - 2 \cos B - 2 \cos C\) (Randy Hutson, 9/23/2011)

▸ Incident Central Lines21 lines

{1, 3}, {4, 1389}, {6, 1411}, {7, 528}, {8, 12}, {33, 1875}, {34, 1824}, {42, 1457}, {45, 1405}, {80, 381}, {145, 388}, {226, 519}, {515, 1836}, {674, 1469}, {758, 956}, {946, 1837}, {952, 1478}, {959, 1255}, {1149, 1450}, {1392, 1476}, {1399, 1468}

▸ Functional Relations5 relations