X2487
RADICAL CENTER OF {INCIRCLE, 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) { 649, 1638 }: Central Line L(649, 1638) { 1125, 1499 }: Central Line L(1125, 1499) { 514, 2516 }: Central Line L(514, 2516) { 918, 2490 }: Central Line L(918, 2490) { 2496, 2505 }: Central Line L(2496, 2505)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_1638 = TRIPOLAR CENTROID OF X(7) (1.6871, 0.9998) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_1499 = POINT BIHAM (0.1078, 0.5997) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (5.0357, 0.5249) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-5.7092, 3.2243) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-1.8622, 2.2579) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5051, -0.1583) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241)
A
B
C
X37
X523
X649
X1638
X1125
X1499
X514
X2516
X918
X2490
X2496
X2505
X2487
(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) { 649, 1638 }: Central Line L(649, 1638) { 1125, 1499 }: Central Line L(1125, 1499) { 514, 2516 }: Central Line L(514, 2516) { 918, 2490 }: Central Line L(918, 2490) { 2496, 2505 }: Central Line L(2496, 2505)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0987, -0.0010) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-8.0000, 6.0000) X_1638 = TRIPOLAR CENTROID OF X(7) (1.4133, 0.5600) X_1125 = COMPLEMENT OF X(10) (0.5600, 0.1700) X_1499 = POINT BIHAM (0.1725, 0.5966) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0889, -0.0314) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (2.8000, 0.6000) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0687, 0.4010) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.2400, 1.3200) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-0.2800, 1.0400) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5600, -0.0800) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-0.9400, 1.9200)
A
B
C
X37
X523
X649
X1638
X1125
X1499
X514
X2516
X918
X2490
X2496
X2505
X2487
(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) { 649, 1638 }: Central Line L(649, 1638) { 1125, 1499 }: Central Line L(1125, 1499) { 514, 2516 }: Central Line L(514, 2516) { 918, 2490 }: Central Line L(918, 2490) { 2496, 2505 }: Central Line L(2496, 2505)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0981, 0.0262) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-9.6244, 5.9482) X_1638 = TRIPOLAR CENTROID OF X(7) (1.5587, 0.5627) X_1125 = COMPLEMENT OF X(10) (0.5505, 0.1720) X_1499 = POINT BIHAM (0.1270, 0.5627) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0910, -0.0001) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (3.2686, 0.5855) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0745, 0.3723) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-2.7661, 1.3080) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (-0.4485, 1.0305) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5350, -0.0651) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-1.2371, 1.9090)
A
B
C
X37
X523
X649
X1638
X1125
X1499
X514
X2516
X918
X2490
X2496
X2505
X2487
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) { 649, 1638 }: Central Line L(649, 1638) { 1125, 1499 }: Central Line L(1125, 1499) { 514, 2516 }: Central Line L(514, 2516) { 918, 2490 }: Central Line L(918, 2490) { 2496, 2505 }: Central Line L(2496, 2505)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_523 = ISOGONAL CONJUGATE OF X(110) (1.1957, 0.0148) X_649 = CROSSDIFFERENCE OF X(1) and X(2) (-2.9286, 1.6903) X_1638 = TRIPOLAR CENTROID OF X(7) (1.3106, 0.2234) X_1125 = COMPLEMENT OF X(10) (0.5621, 0.1025) X_1499 = POINT BIHAM (0.1913, 0.6463) X_514 = ISOGONAL CONJUGATE OF X(101) (1.1917, -0.0133) X_2516 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (1.8599, 0.3251) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.1912, 0.2031) X_2490 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, SPIEKER CIRCLE} (-0.8985, 0.3951) X_2496 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, SPIEKER CIRCLE} (0.3681, 0.3629) X_2505 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, SPIEKER CIRCLE} (0.5674, -0.0229) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (0.2508, 0.5901)
A
B
C
X37
X523
X649
X1638
X1125
X1499
X514
X2516
X918
X2490
X2496
X2505
X2487
Kimberling (6, 9, 13) | AB = 1
X2487 (RADICAL CENTER OF {INCIRCLE, 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 \(f(a,b,c) = bc(b - c)[(b - c)^{2} + ab + ac - 4a^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-0.187812056606\)
▸ Incident Central Lines5 lines
▸ Functional Relations3 relations
