X2524
RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd 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) { 2489, 2507 }: Central Line L(2489, 2507) { 39, 512 }: Central Line L(39, 512) { 441, 525 }: Central Line L(441, 525)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.1726, 0.9764) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.8163, 0.3364) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2524 = RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd BROCARD} CIRCLES (1.4600, -0.3036)
A
B
C
X2489
X2507
X39
X512
X441
X525
X2524
(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) { 2489, 2507 }: Central Line L(2489, 2507) { 39, 512 }: Central Line L(39, 512) { 441, 525 }: Central Line L(441, 525)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.6400, 0.4800) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.7941, 0.2400) X_39 = BROCARD MIDPOINT (0.6138, 0.1951) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_2524 = RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd BROCARD} CIRCLES (0.9482, 0.0000)
A
B
C
X2489
X2507
X39
X512
X441
X525
X2524
(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) { 2489, 2507 }: Central Line L(2489, 2507) { 39, 512 }: Central Line L(39, 512) { 441, 525 }: Central Line L(441, 525)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.6180, 0.4859) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.8090, 0.2429) X_39 = BROCARD MIDPOINT (0.5955, 0.1965) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_2524 = RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd BROCARD} CIRCLES (1.0000, 0.0000)
A
B
C
X2489
X2507
X39
X512
X441
X525
X2524
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) { 2489, 2507 }: Central Line L(2489, 2507) { 39, 512 }: Central Line L(39, 512) { 441, 525 }: Central Line L(441, 525)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2489 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE} (0.8221, 0.1876) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.7934, 0.1329) X_39 = BROCARD MIDPOINT (0.6418, 0.1220) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_2524 = RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd BROCARD} CIRCLES (0.7647, 0.0781)
A
B
C
X2489
X2507
X39
X512
X441
X525
X2524
Kimberling (6, 9, 13) | AB = 1
X2524 (RADICAL CENTER OF {NINE-POINT, BROCARD, 2nd 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 \(f(a,b,c) = a(b^{2} - c^{2})(b^{2} + c^{2} - a^{2})(b^{2}c^{2} - a^{2}b^{2} - a^{2}c^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(1.049203571144\)
▸ Incident Central Lines3 lines
▸ Functional Relations2 relations
