X2529
RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} 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) { 2516, 2537 }: Central Line L(2516, 2537) { 514, 2487 }: Central Line L(514, 2487) { 650, 2457 }: Central Line L(650, 2457)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (5.0357, 0.5249) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4272, -0.1877) 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_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (-1.5941, 2.6476) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-51.1684, 24.8198)
A
B
C
X2516
X2537
X514
X2487
X650
X2457
X2529
(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) { 2516, 2537 }: Central Line L(2516, 2537) { 514, 2487 }: Central Line L(514, 2487) { 650, 2457 }: Central Line L(650, 2457)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (2.8000, 0.6000) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4076, -0.6465) 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_650 = CROSSDIFFERENCE OF X(1) AND X(3) (6.4000, -1.2000) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.1600, 1.1200) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-21.6800, 9.2400)
A
B
C
X2516
X2537
X514
X2487
X650
X2457
X2529
(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) { 2516, 2537 }: Central Line L(2516, 2537) { 514, 2487 }: Central Line L(514, 2487) { 650, 2457 }: Central Line L(650, 2457)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (3.2686, 0.5855) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.4224, -0.6480) 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_650 = CROSSDIFFERENCE OF X(1) AND X(3) (7.5663, -1.2021) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.0441, 1.1253) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-25.9916, 9.1808)
A
B
C
X2516
X2537
X514
X2487
X650
X2457
X2529
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) { 2516, 2537 }: Central Line L(2516, 2537) { 514, 2487 }: Central Line L(514, 2487) { 650, 2457 }: Central Line L(650, 2457)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (1.8599, 0.3251) X_2537 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER RADICAL CIRCLE) (0.6801, 6.8228) 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_650 = CROSSDIFFERENCE OF X(1) AND X(3) (3.4560, -0.1300) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.8916, 0.3289) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-10.0415, 2.2854)
A
B
C
X2516
X2537
X514
X2487
X650
X2457
X2529
Kimberling (6, 9, 13) | AB = 1
X2529 (RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} 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 \(f(a,b,c) = bc(b - c)(7a^{2} + ab + ac + 2(b + c)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(63.480475132942\)
▸ Incident Central Lines2 lines
▸ Functional Relations1 relation
