X2516
RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE}
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) { 44, 513 }: Central Line L(44, 513) { 514, 2487 }: Central Line L(514, 2487) { 522, 2490 }: Central Line L(522, 2490)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0318, 0.3430) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (5.0357, 0.5249)
A
B
C
X44
X513
X514
X2487
X522
X2490
X2516
(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) { 44, 513 }: Central Line L(44, 513) { 514, 2487 }: Central Line L(514, 2487) { 522, 2490 }: Central Line L(522, 2490)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0889, -0.0314) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-0.9400, 1.9200) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0226, 0.2413) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.2400, 1.3200) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (2.8000, 0.6000)
A
B
C
X44
X513
X514
X2487
X522
X2490
X2516
(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) { 44, 513 }: Central Line L(44, 513) { 514, 2487 }: Central Line L(514, 2487) { 522, 2490 }: Central Line L(522, 2490)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0910, -0.0001) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-1.2371, 1.9090) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.0316, 0.2303) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.7661, 1.3080) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (3.2686, 0.5855)
A
B
C
X44
X513
X514
X2487
X522
X2490
X2516
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) { 44, 513 }: Central Line L(44, 513) { 514, 2487 }: Central Line L(514, 2487) { 522, 2490 }: Central Line L(522, 2490)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_514 = ISOGONAL CONJUGATE OF X(101) (1.1917, -0.0133) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (0.2508, 0.5901) X_522 = ISOGONAL CONJUGATE OF X(109) (-0.1115, 0.1100) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-0.8985, 0.3951) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (1.8599, 0.3251)
A
B
C
X44
X513
X514
X2487
X522
X2490
X2516
Kimberling (6, 9, 13) | AB = 1
X2516 (RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN 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 \(f(a,b,c) = (b - c)(5a - 3b -3c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-10.141851056742\)
▸ Incident Central Lines3 lines
▸ Functional Relations3 relations
