X2521
RADICAL CENTER OF {BROCARD, BEVAN,MOSES} 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) { 512, 2031 }: Central Line L(512, 2031) { 649, 2523 }: Central Line L(649, 2523)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) 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_649 = CROSSDIFFERENCE OF X(1) and X(2) (-21.0000, 14.6969) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (6.2080, -0.7560) X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES (-71.3829, 43.3121)
A
B
C
X512
X2031
X649
X2523
X2521
(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) { 512, 2031 }: Central Line L(512, 2031) { 649, 2523 }: Central Line L(649, 2523)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) 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_649 = CROSSDIFFERENCE OF X(1) and X(2) (-8.0000, 6.0000) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (3.2941, 0.0000) X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES (-25.9626, 15.5426)
A
B
C
X512
X2031
X649
X2523
X2521
(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) { 512, 2031 }: Central Line L(512, 2031) { 649, 2523 }: Central Line L(649, 2523)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) 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_649 = CROSSDIFFERENCE OF X(1) and X(2) (-9.6244, 5.9482) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (3.8272, 0.0000) X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES (-31.4675, 15.6071)
A
B
C
X512
X2031
X649
X2523
X2521
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) { 512, 2031 }: Central Line L(512, 2031) { 649, 2523 }: Central Line L(649, 2523)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) 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_649 = CROSSDIFFERENCE OF X(1) and X(2) (-2.9286, 1.6903) X_2523 = RADICAL CENTER OF {NINE-POINT,BROCARD, BEVAN} CIRCLES (2.1047, 0.1270) X_2521 = RADICAL CENTER OF {BROCARD, BEVAN,MOSES} CIRCLES (-8.7507, 3.4986)
A
B
C
X512
X2031
X649
X2523
X2521
Kimberling (6, 9, 13) | AB = 1
X2521 (RADICAL CENTER OF {BROCARD, BEVAN,MOSES} 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 \(f(a,b,c) = a(b - c)[2(a^{4} + b^{4} + c^{4}) + 3bc(a^{2} + b^{2} + c^{2} + ab + ac)]\)
Search Value (6, 9, 13): \(40.761600800190\)
▸ Incident Central Lines2 lines
