X2526
RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X4 ,2R)} CIRCLES
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)
{ 650, 1491 }: Central Line L(650, 1491)
{ 44, 513 }: Central Line L(44, 513)
{ 830, 905 }: Central Line L(830, 905)
{ 523, 2525 }: Central Line L(523, 2525)
A = Vertex A (0.0000, 0.0000)
B = Vertex B (1.0000, 0.0000)
C = Vertex C (0.6122, 0.5999)
X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991)
X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (25.5000, -10.6145)
X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996)
X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806)
X_830 = ODD (1, 3) INFINITY POINT (1.0590, -0.0690)
X_905 = POINT ACHERNAR (5.6190, -0.6999)
X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096)
X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-9.1140, 0.7037)
X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (37.2857, -17.0298)
A
B
C
X650
X1491
X44
X513
X830
X905
X523
X2525
X2526
(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)
{ 650, 1491 }: Central Line L(650, 1491)
{ 44, 513 }: Central Line L(44, 513)
{ 830, 905 }: Central Line L(830, 905)
{ 523, 2525 }: Central Line L(523, 2525)
A = Vertex A (0.0000, 0.0000)
B = Vertex B (1.0000, 0.0000)
C = Vertex C (0.6400, 0.4800)
X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (6.4000, -1.2000)
X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (11.4000, -3.7000)
X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000)
X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971)
X_830 = ODD (1, 3) INFINITY POINT (1.0685, -0.0815)
X_905 = POINT ACHERNAR (3.0000, 0.0000)
X_523 = ISOGONAL CONJUGATE OF X(110) (1.0987, -0.0010)
X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-4.8571, 0.0000)
X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (16.4000, -6.2000)
A
B
C
X650
X1491
X44
X513
X830
X905
X523
X2525
X2526
(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)
{ 650, 1491 }: Central Line L(650, 1491)
{ 44, 513 }: Central Line L(44, 513)
{ 830, 905 }: Central Line L(830, 905)
{ 523, 2525 }: Central Line L(523, 2525)
A = Vertex A (0.0000, 0.0000)
B = Vertex B (1.0000, 0.0000)
C = Vertex C (0.6180, 0.4859)
X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (7.5663, -1.2021)
X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (13.5145, -3.6762)
X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165)
X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589)
X_830 = ODD (1, 3) INFINITY POINT (1.0760, -0.0445)
X_905 = POINT ACHERNAR (3.4741, 0.0000)
X_523 = ISOGONAL CONJUGATE OF X(110) (1.0981, 0.0262)
X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-5.8541, 0.0000)
X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (19.4627, -6.1503)
A
B
C
X650
X1491
X44
X513
X830
X905
X523
X2525
X2526
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)
{ 650, 1491 }: Central Line L(650, 1491)
{ 44, 513 }: Central Line L(44, 513)
{ 830, 905 }: Central Line L(830, 905)
{ 523, 2525 }: Central Line L(523, 2525)
A = Vertex A (0.0000, 0.0000)
B = Vertex B (1.0000, 0.0000)
C = Vertex C (0.6331, 0.2801)
X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (3.4560, -0.1300)
X_1491 = CROSSDIFFERENCE OF X(1) AND X(32) (5.7851, -0.7941)
X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412)
X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865)
X_830 = ODD (1, 3) INFINITY POINT (1.1800, -0.0690)
X_905 = POINT ACHERNAR (1.9337, 0.1207)
X_523 = ISOGONAL CONJUGATE OF X(110) (1.1957, 0.0148)
X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-3.3742, -0.0728)
X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (8.1142, -1.4581)
A
B
C
X650
X1491
X44
X513
X830
X905
X523
X2525
X2526
Kimberling (6, 9, 13) | AB = 1
X2526 (RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X4 ,2R)} CIRCLES ) 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 \(f(a,b,c) = (b - c)(a^{2} + 3b^{2} + 2bc + 3c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-41.050349515385\)
▸ Incident Central Lines3 lines
▸ Functional Relations2 relations