X2515
RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD 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) { 2483, 2484 }: Central Line L(2483, 2484) { 44, 513 }: Central Line L(44, 513) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-28.3636, 18.7052) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-35.7273, 22.7135) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.8993, 0.7615) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-32.0455, 20.7093)
A
B
C
X2483
X2484
X44
X513
X512
X2030
X2515
(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) { 2483, 2484 }: Central Line L(2483, 2484) { 44, 513 }: Central Line L(44, 513) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-10.8800, 7.4400) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-13.7600, 8.8800) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.7967, 0.5086) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-12.3200, 8.1600)
A
B
C
X2483
X2484
X44
X513
X512
X2030
X2515
(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) { 2483, 2484 }: Central Line L(2483, 2484) { 44, 513 }: Central Line L(44, 513) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-13.0985, 7.3933) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-16.5727, 8.8383) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.7613, 0.5377) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-14.8356, 8.1158)
A
B
C
X2483
X2484
X44
X513
X512
X2030
X2515
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) { 2483, 2484 }: Central Line L(2483, 2484) { 44, 513 }: Central Line L(44, 513) { 512, 2030 }: Central Line L(512, 2030)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-4.0480, 2.0095) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-5.1673, 2.3286) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.6959, 0.2732) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-4.6076, 2.1690)
A
B
C
X2483
X2484
X44
X513
X512
X2030
X2515
Kimberling (6, 9, 13) | AB = 1
X2515 (RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD 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 \(f(a,b,c) = a(b - c)(2a^{2} + 2b^{2} + 2c^{2} + 3bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(21.820346212991\)
▸ Incident Central Lines2 lines
▸ Functional Relations2 relations
