X2504
RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE}
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) { 11, 244 }: Central Line L(11, 244) { 441, 525 }: Central Line L(441, 525) { 2473, 2488 }: Central Line L(2473, 2488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_244 = -LINE CONJUGATE OF X(100) (0.7857, 0.1166) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (21.7939, -9.6080) X_2488 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD} (12.0571, -5.3189) X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} (0.4545, -0.2079)
A
B
C
X11
X244
X441
X525
X2473
X2488
X2504
(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) { 11, 244 }: Central Line L(11, 244) { 441, 525 }: Central Line L(441, 525) { 2473, 2488 }: Central Line L(2473, 2488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_11 = FEUERBACH POINT (0.7200, 0.0400) X_244 = -LINE CONJUGATE OF X(100) (0.8000, 0.1000) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (9.6000, -3.3500) X_2488 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD} (5.2000, -1.7000) X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} (0.6667, 0.0000)
A
B
C
X11
X244
X441
X525
X2473
X2488
X2504
(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) { 11, 244 }: Central Line L(11, 244) { 441, 525 }: Central Line L(441, 525) { 2473, 2488 }: Central Line L(2473, 2488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_11 = FEUERBACH POINT (0.6897, 0.0298) X_244 = -LINE CONJUGATE OF X(100) (0.7719, 0.0802) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (11.3469, -3.3252) X_2488 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD} (6.1212, -1.7021) X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} (0.6411, 0.0000)
A
B
C
X11
X244
X441
X525
X2473
X2488
X2504
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) { 11, 244 }: Central Line L(11, 244) { 441, 525 }: Central Line L(441, 525) { 2473, 2488 }: Central Line L(2473, 2488)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_11 = FEUERBACH POINT (0.6563, 0.0066) X_244 = -LINE CONJUGATE OF X(100) (0.7876, 0.0501) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_2473 = RADICAL CENTER OF {BROCARD CIRCLE, BEVAN CIRCLE, INCIRCLE} (4.6725, -0.6706) X_2488 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, BROCARD} (2.4264, -0.2239) X_2504 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} (0.8854, 0.0825)
A
B
C
X11
X244
X441
X525
X2473
X2488
X2504
Kimberling (6, 9, 13) | AB = 1
X2504 (RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, BROCARD CIRCLE} ) 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 \(f(a,b,c) = bc(b - c)(b^{2} + c^{2} - a^{2})[2a^{3} + (b + c)(b - c - a)(b - c + a)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.051167129362\)
▸ Incident Central Lines3 lines
