X2483
RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE 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) { 2484, 2515 }: Central Line L(2484, 2515) { 44, 513 }: Central Line L(44, 513) { 918, 1019 }: Central Line L(918, 1019) { 512, 1691 }: Central Line L(512, 1691) { 1919, 2605 }: Central Line L(1919, 2605)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-35.7273, 22.7135) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-32.0455, 20.7093) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0192, 0.5351) X_1019 = -CEVA CONJUGATE OF X(1) (-29.0952, 18.1962) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.9991, 0.9263) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-2.5853, 3.3187) X_2605 = DIFFERENCE OF PU(71) (6.1667, -1.9052) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-28.3636, 18.7052)
A
B
C
X2484
X2515
X44
X513
X918
X1019
X512
X1691
X1919
X2605
X2483
(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) { 2484, 2515 }: Central Line L(2484, 2515) { 44, 513 }: Central Line L(44, 513) { 918, 1019 }: Central Line L(918, 1019) { 512, 1691 }: Central Line L(512, 1691) { 1919, 2605 }: Central Line L(1919, 2605)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-13.7600, 8.8800) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-12.3200, 8.1600) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0687, 0.4010) X_1019 = -CEVA CONJUGATE OF X(1) (-11.4000, 7.2000) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.8489, 0.5981) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-0.5773, 1.5464) X_2605 = DIFFERENCE OF PU(71) (3.0000, -0.5000) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-10.8800, 7.4400)
A
B
C
X2484
X2515
X44
X513
X918
X1019
X512
X1691
X1919
X2605
X2483
(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) { 2484, 2515 }: Central Line L(2484, 2515) { 44, 513 }: Central Line L(44, 513) { 918, 1019 }: Central Line L(918, 1019) { 512, 1691 }: Central Line L(512, 1691) { 1919, 2605 }: Central Line L(1919, 2605)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-16.5727, 8.8383) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-14.8356, 8.1158) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.0745, 0.3723) X_1019 = -CEVA CONJUGATE OF X(1) (-13.7166, 7.1503) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.8090, 0.6360) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-0.7862, 1.5291) X_2605 = DIFFERENCE OF PU(71) (3.4741, -0.5000) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-13.0985, 7.3933)
A
B
C
X2484
X2515
X44
X513
X918
X1019
X512
X1691
X1919
X2605
X2483
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) { 2484, 2515 }: Central Line L(2484, 2515) { 44, 513 }: Central Line L(44, 513) { 918, 1019 }: Central Line L(918, 1019) { 512, 1691 }: Central Line L(512, 1691) { 1919, 2605 }: Central Line L(1919, 2605)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-5.1673, 2.3286) X_2515 = RADICAL CENTER OF {CIRCUMCIRCLE, BEVAN CIRCLE, 2nd BROCARD CIRCLE} (-4.6076, 2.1690) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_918 = ISOTOMIC CONJUGATE OF X(666) (1.1912, 0.2031) X_1019 = -CEVA CONJUGATE OF X(1) (-4.4509, 1.9411) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.7087, 0.3091) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (0.1852, 0.5339) X_2605 = DIFFERENCE OF PU(71) (1.7294, -0.0043) X_2483 = RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE CIRCLE, BEVAN CIRCLE} (-4.0480, 2.0095)
A
B
C
X2484
X2515
X44
X513
X918
X1019
X512
X1691
X1919
X2605
X2483
Kimberling (6, 9, 13) | AB = 1
X2483 (RADICAL CENTER OF {CIRCUMCIRCLE, 1st LEMOINE 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 \(f(a,b,c) = a(b - c)(a^{2} + b^{2} + c^{2} + bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(19.054386833879\)
▸ Incident Central Lines4 lines
▸ Functional Relations3 relations
