X2510
RADICAL CENTER OF {NINE-POINT, BROCARD, 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) { 115, 804 }: Central Line L(115, 804) { 441, 525 }: Central Line L(441, 525) { 248, 878 }: Central Line L(248, 878) { 512, 2031 }: Central Line L(512, 2031)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_804 = ODD (- 2, 2) INFINITY POINT (0.9171, 0.6474) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_878 = ISOGONAL CONJUGATE OF X(877) (1.1192, 0.0431) 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_2510 = RADICAL CENTER OF {NINE-POINT, BROCARD, MOSES} CIRCLES (0.4995, -0.2121)
A
B
C
X115
X804
X441
X525
X248
X878
X512
X2031
X2510
(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) { 115, 804 }: Central Line L(115, 804) { 441, 525 }: Central Line L(441, 525) { 248, 878 }: Central Line L(248, 878) { 512, 2031 }: Central Line L(512, 2031)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7445, 0.0609) X_804 = ODD (- 2, 2) INFINITY POINT (0.9585, 0.5612) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_248 = -LINE CONJUGATE OF X(132) (0.7596, 0.0000) X_878 = ISOGONAL CONJUGATE OF X(877) (1.2165, 0.0000) 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_2510 = RADICAL CENTER OF {NINE-POINT, BROCARD, MOSES} CIRCLES (0.6819, 0.0000)
A
B
C
X115
X804
X441
X525
X248
X878
X512
X2031
X2510
(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) { 115, 804 }: Central Line L(115, 804) { 441, 525 }: Central Line L(441, 525) { 248, 878 }: Central Line L(248, 878) { 512, 2031 }: Central Line L(512, 2031)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7135, 0.0464) X_804 = ODD (- 2, 2) INFINITY POINT (0.9914, 0.5173) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_248 = -LINE CONJUGATE OF X(132) (0.7236, 0.0000) X_878 = ISOGONAL CONJUGATE OF X(877) (1.3090, 0.0000) 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_2510 = RADICAL CENTER OF {NINE-POINT, BROCARD, MOSES} CIRCLES (0.6545, 0.0000)
A
B
C
X115
X804
X441
X525
X248
X878
X512
X2031
X2510
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) { 115, 804 }: Central Line L(115, 804) { 441, 525 }: Central Line L(441, 525) { 248, 878 }: Central Line L(248, 878) { 512, 2031 }: Central Line L(512, 2031)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_115 = CENTER OF KIEPERT HYPERBOLA (0.6909, 0.0207) X_804 = ODD (- 2, 2) INFINITY POINT (1.1348, 0.3793) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_248 = -LINE CONJUGATE OF X(132) (0.6841, 0.1154) X_878 = ISOGONAL CONJUGATE OF X(877) (1.9152, -0.2231) 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_2510 = RADICAL CENTER OF {NINE-POINT, BROCARD, MOSES} CIRCLES (0.8132, 0.0799)
A
B
C
X115
X804
X441
X525
X248
X878
X512
X2031
X2510
Kimberling (6, 9, 13) | AB = 1
X2510 (RADICAL CENTER OF {NINE-POINT, BROCARD, 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 \(f(a,b,c) = a(b^{2} + c^{2} - a^{2})(b^{2} - c^{2})(a^{4} + b^{4} + c^{4} - 3b^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.648094501847\)
▸ Incident Central Lines4 lines
