X2557
2nd INTERSECTION(LINE X1 X_3, 2nd BROCARD CIRCLE)
Of the two points of intersection,
X2557 is one farther from
X1 .
5, 6, 7
3, 4, 5
Kepler
Kimberling
< 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) { 2556, 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_2556 = 1st INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.5108, 0.1220) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_1 = INCENTER (0.5714, 0.2333) X_2557 = 2nd INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.4892, 0.0822)
A
B
C
X2556
X3
X1
X2557
(a, b, c) = (5, 6, 7) | AB = 1
< 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) { 2556, 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 (0.6400, 0.4800) X_2556 = 1st INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.5200, 0.0401) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_1 = INCENTER (0.6000, 0.2000) X_2557 = 2nd INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.4800, -0.0401)
A
B
C
X2556
X3
X1
X2557
(a, b, c) = (3, 4, 5) | AB = 1
< 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) { 2556, 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 (0.6180, 0.4859) X_2556 = 1st INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.5505, 0.1214) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_1 = INCENTER (0.5841, 0.2021) X_2557 = 2nd INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.4495, -0.1214)
A
B
C
X2556
X3
X1
X2557
Kepler (1, √φ, φ) | AB = 1
< 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) { 2556, 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 (0.6331, 0.2801) X_2556 = 1st INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.5062, -0.2529) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_1 = INCENTER (0.6154, 0.1300) X_2557 = 2nd INTERSECTION(LINE X(1)X(3), 2nd BROCARD CIRCLE) (0.4938, -0.2965)
A
B
C
X2556
X3
X1
X2557
Kimberling (6, 9, 13) | AB = 1
X2557 (2nd INTERSECTION(LINE X1 X_3, 2nd BROCARD CIRCLE) ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(f(A,B,C) : f(B,C,A) : f(C,A,B)\) , where
\(f(A,B,C) = 1 - \cos B - \cos C + (d/e) \cos A\) , where d, e are as at
X2556 Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(7.056348338294\)
▸ Incident Central Lines1 line
▸ Functional Relations1 relation
