X2527
RADICAL CENTER OF {NINE-POINT, 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, 2529 }: Central Line L(2516, 2529) { 649, 900 }: Central Line L(649, 900) { 514, 2487 }: Central Line L(514, 2487) { 513, 2490 }: Central Line L(513, 2490) { 650, 2523 }: Central Line L(650, 2523)
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_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-51.1684, 24.8198) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (0.9566, 0.6107) 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_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (6.2080, -0.7560) X_2527 = RADICAL CENTER OF {NINE-POINT, SPIEKER, BEVAN} CIRCLES (-23.0663, 12.6724)
A
B
C
X2516
X2529
X649
X900
X514
X2487
X513
X2490
X650
X2523
X2527
(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, 2529 }: Central Line L(2516, 2529) { 649, 900 }: Central Line L(649, 900) { 514, 2487 }: Central Line L(514, 2487) { 513, 2490 }: Central Line L(513, 2490) { 650, 2523 }: Central Line L(650, 2523)
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_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-21.6800, 9.2400) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-8.0000, 6.0000) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (1.0067, 0.5050) 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_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.2400, 1.3200) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (6.4000, -1.2000) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (3.2941, 0.0000) X_2527 = RADICAL CENTER OF {NINE-POINT, SPIEKER, BEVAN} CIRCLES (-9.4400, 4.9200)
A
B
C
X2516
X2529
X649
X900
X514
X2487
X513
X2490
X650
X2523
X2527
(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, 2529 }: Central Line L(2516, 2529) { 649, 900 }: Central Line L(649, 900) { 514, 2487 }: Central Line L(514, 2487) { 513, 2490 }: Central Line L(513, 2490) { 650, 2523 }: Central Line L(650, 2523)
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_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-25.9916, 9.1808) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-9.6244, 5.9482) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (1.0295, 0.4625) 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_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.7661, 1.3080) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (7.5663, -1.2021) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (3.8272, 0.0000) X_2527 = RADICAL CENTER OF {NINE-POINT, SPIEKER, BEVAN} CIRCLES (-11.3615, 4.8832)
A
B
C
X2516
X2529
X649
X900
X514
X2487
X513
X2490
X650
X2523
X2527
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, 2529 }: Central Line L(2516, 2529) { 649, 900 }: Central Line L(649, 900) { 514, 2487 }: Central Line L(514, 2487) { 513, 2490 }: Central Line L(513, 2490) { 650, 2523 }: Central Line L(650, 2523)
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_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-10.0415, 2.2854) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-2.9286, 1.6903) X_900 = CROSSDIFFERENCE OF X(6) AND X(101) (1.1671, 0.2997) 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_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-0.8985, 0.3951) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (3.4560, -0.1300) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (2.1047, 0.1270) X_2527 = RADICAL CENTER OF {NINE-POINT, SPIEKER, BEVAN} CIRCLES (-4.0908, 1.3052)
A
B
C
X2516
X2529
X649
X900
X514
X2487
X513
X2490
X650
X2523
X2527
Kimberling (6, 9, 13) | AB = 1
X2527 (RADICAL CENTER OF {NINE-POINT, 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 \(f(a,b,c) = bc(b - c)(6a^{2} - ab - ac + (b + c)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(26.669312038100\)
▸ Incident Central Lines4 lines
▸ Functional Relations1 relation
