X2518
RADICAL CENTER OF {BROCARD, MOSES, (X4 ,2R)} 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) { 211, 688 }: Central Line L(211, 688) { 512, 2031 }: Central Line L(512, 2031) { 826, 2474 }: Central Line L(826, 2474)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_211 = -CEVA CONJUGATE OF X(39) (0.6801, 0.4536) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.0103, -0.1475) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_2031 = RADICAL TRACE OF MOSES AND BROCARD CIRCLES (0.3607, -0.1281) X_826 = ODD (0, 4) INFINITY POINT (1.1003, 0.0340) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (6.9649, -4.0371) X_2518 = RADICAL CENTER OF {BROCARD, MOSES, (X(4),2R)} CIRCLES (6.6758, -3.9518)
A
B
C
X211
X688
X512
X2031
X826
X2474
X2518
(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) { 211, 688 }: Central Line L(211, 688) { 512, 2031 }: Central Line L(512, 2031) { 826, 2474 }: Central Line L(826, 2474)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_211 = -CEVA CONJUGATE OF X(39) (0.7029, 0.4678) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.0049, -0.1873) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_2031 = RADICAL TRACE OF MOSES AND BROCARD CIRCLES (0.5462, 0.0792) X_826 = ODD (0, 4) INFINITY POINT (1.1111, 0.0502) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (3.3886, -1.6033) X_2518 = RADICAL CENTER OF {BROCARD, MOSES, (X(4),2R)} CIRCLES (3.4514, -1.6156)
A
B
C
X211
X688
X512
X2031
X826
X2474
X2518
(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) { 211, 688 }: Central Line L(211, 688) { 512, 2031 }: Central Line L(512, 2031) { 826, 2474 }: Central Line L(826, 2474)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_211 = -CEVA CONJUGATE OF X(39) (0.6727, 0.4770) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.0245, -0.1466) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_2031 = RADICAL TRACE OF MOSES AND BROCARD CIRCLES (0.5295, 0.0607) X_826 = ODD (0, 4) INFINITY POINT (1.1069, 0.0700) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (3.8541, -1.5723) X_2518 = RADICAL CENTER OF {BROCARD, MOSES, (X(4),2R)} CIRCLES (3.9088, -1.5812)
A
B
C
X211
X688
X512
X2031
X826
X2474
X2518
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) { 211, 688 }: Central Line L(211, 688) { 512, 2031 }: Central Line L(512, 2031) { 826, 2474 }: Central Line L(826, 2474)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_211 = -CEVA CONJUGATE OF X(39) (0.6057, 0.3867) X_688 = CROSSDIFFERENCE OF X(6) AND X(76) (1.1304, -0.2016) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_2031 = RADICAL TRACE OF MOSES AND BROCARD CIRCLES (0.6479, 0.1390) X_826 = ODD (0, 4) INFINITY POINT (1.1992, 0.0530) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (2.0285, -0.4057) X_2518 = RADICAL CENTER OF {BROCARD, MOSES, (X(4),2R)} CIRCLES (2.2012, -0.4163)
A
B
C
X211
X688
X512
X2031
X826
X2474
X2518
Kimberling (6, 9, 13) | AB = 1
X2518 (RADICAL CENTER OF {BROCARD, MOSES, (X4 ,2R)} 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 \(f(a,b,c) = a(b^{4} - c^{4})(2a^{4} + 2b^{4} + 2c^{4} - 3b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-5.173787305578\)
▸ Incident Central Lines3 lines
