X2519
RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} 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) { 441, 525 }: Central Line L(441, 525) { 512, 1570 }: Central Line L(512, 1570)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.4005, -0.0623) X_2519 = RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} CIRCLES (0.6756, -0.2289)
A
B
C
X441
X525
X512
X1570
X2519
(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) { 441, 525 }: Central Line L(441, 525) { 512, 1570 }: Central Line L(512, 1570)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.5355, 0.0609) X_2519 = RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} CIRCLES (0.6400, 0.0000)
A
B
C
X441
X525
X512
X1570
X2519
(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) { 441, 525 }: Central Line L(441, 525) { 512, 1570 }: Central Line L(512, 1570)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.5225, 0.0464) X_2519 = RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} CIRCLES (0.6180, 0.0000)
A
B
C
X441
X525
X512
X1570
X2519
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) { 441, 525 }: Central Line L(441, 525) { 512, 1570 }: Central Line L(512, 1570)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.6317, 0.0937) X_2519 = RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} CIRCLES (0.6835, 0.0752)
A
B
C
X441
X525
X512
X1570
X2519
Kimberling (6, 9, 13) | AB = 1
X2519 (RADICAL CENTER OF {NINE-POINT, 2nd LEMOINE, BROCARD} 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 \(f(a,b,c) = a(b^{2} - c^{2})(b^{2} + c^{2} - a^{2})(a^{4} + b^{4} + c^{4} + 2a^{2}b^{2} + 2a^{2}c^{2} - 6b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.720257139275\)
▸ Incident Central Lines2 lines
