X2446

1st INTERSECTION(LINE X1X_3, INCIRCLE)

Of the two points of intersection, X2446 is the closer to X3.
< 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) { 2447, 1 }: OI Line (Incenter–Circumcenter Line) { 1, 3 }: OI Line (Incenter–Circumcenter Line) { 2170, 2590 }: Central Line L(2170, 2590) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2447 = 2nd INTERSECTION(LINE X(1)X(3), INCIRCLE) (0.6830, 0.4382) X_1 = INCENTER (0.5714, 0.2333) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_2170 = -ISOCONJUGATE OF X(59) (0.7601, 0.0792) X_2590 = -ISOCONJUGATE OF X(1381) (4.6456, 0.7372) X_2446 = 1st INTERSECTION(LINE X(1)X(3), INCIRCLE) (0.4599, 0.0284) A B C X2447 X1 X3 X2170 X2590 X2446 (a, b, c) = (5, 6, 7) | AB = 1

X2446 (1st INTERSECTION(LINE X1X_3, INCIRCLE)) 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 \(f(A,B,C) = \cos B + \cos C - 1 - D\), \(D = (3 - 2 \cos A - 2 \cos B - 2 \cos C)^{1/2}\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.263612986634\)

X2446 lies on the incircle.

▸ Incident Central Lines2 lines

{1, 3}, {2170, 2590}

▸ Functional Relations4 relations