X1482

REFLECTION OF CIRCUMCENTER IN INCENTER

X1482 is the reflection of circumcenter in incenter.
< 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) { 3, 1 }: OI Line (Incenter–Circumcenter Line) { 5, 8 }: Central Line L(5, 8) { 4, 145 }: Central Line L(4, 145) { 355, 381 }: Central Line L(355, 381) { 382, 515 }: Central Line L(382, 515) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1 = INCENTER (0.5714, 0.2333) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_8 = NAGEL POINT (0.4694, 0.1333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_145 = ANTICOMPLEMENT OF NAGEL POINT (0.6735, 0.3333) X_355 = FUHRMANN CENTER (0.5408, 0.2645) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_382 = REFLECTION OF CIRCUMCENTER IN ORTHOCENTER (0.7245, 0.6894) X_515 = ISOGONAL CONJUGATE OF X(102) (0.6804, 0.7691) X_1482 = REFLECTION OF CIRCUMCENTER IN INCENTER (0.6429, 0.3645) A B C X3 X1 X5 X8 X4 X145 X355 X381 X382 X515 X1482 (a, b, c) = (5, 6, 7) | AB = 1

X1482 (REFLECTION OF CIRCUMCENTER IN INCENTER) 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 \(f(a,b,c) = 2r - R \cos A (where r\)= inradius, R = circumradius)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-3.401745875282\)
▸ Incident Central Lines8 lines

{1, 3}, {4, 145}, {5, 8}, {30, 944}, {104, 1392}, {355, 381}, {382, 515}, {518, 1351}

▸ Functional Relations6 relations