X1381

1st INTERCEPT OF LINE X1X_3 AND CIRCUMCIRCLE

The line IO, where I = X1 = incenter and O = X3 = circumcenter, meets the circumcircle in two points, X1381 and X1382, where X1381 is the nearer of the two to 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) { 1382, 3 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1382 = 2nd INTERCEPT OF LINE X(1)X(3) AND CIRCUMCIRCLE (0.2560, -0.3461) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1 = INCENTER (0.5714, 0.2333) X_1381 = 1st INTERCEPT OF LINE X(1)X(3) AND CIRCUMCIRCLE (0.7440, 0.5503) A B C X1382 X3 X1 X1381 (a, b, c) = (5, 6, 7) | AB = 1

X1381 (1st INTERCEPT OF LINE X1X_3 AND CIRCUMCIRCLE) 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 \(f(a,b,c) = r + (|OI| - R) \cos A\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.120510499417\)

X1381 lies on the circumcircle.

▸ Incident Central Lines1 line

{1, 3}

▸ Functional Relations4 relations