X2486
RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE}
X2486 = intersection of tangents to nine-point circle at
X11 and
X115
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) { 115, 804 }: Central Line L(115, 804) { 5, 2783 }: Central Line L(5, 2783)
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_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_804 = ODD (- 2, 2) INFINITY POINT (0.9171, 0.6474) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.9670, -0.1999) X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE} (0.7431, 0.0749)
A
B
C
X11
X244
X115
X804
X5
X2783
X2486
(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) { 115, 804 }: Central Line L(115, 804) { 5, 2783 }: Central Line L(5, 2783)
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_115 = CENTER OF KIEPERT HYPERBOLA (0.7445, 0.0609) X_804 = ODD (- 2, 2) INFINITY POINT (0.9585, 0.5612) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.9206, -0.2768) X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE} (0.7329, 0.0497)
A
B
C
X11
X244
X115
X804
X5
X2783
X2486
(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) { 115, 804 }: Central Line L(115, 804) { 5, 2783 }: Central Line L(5, 2783)
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_115 = CENTER OF KIEPERT HYPERBOLA (0.7135, 0.0464) X_804 = ODD (- 2, 2) INFINITY POINT (0.9914, 0.5173) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.2108, 0.6339) X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE} (0.7021, 0.0374)
A
B
C
X11
X244
X115
X804
X5
X2783
X2486
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) { 115, 804 }: Central Line L(115, 804) { 5, 2783 }: Central Line L(5, 2783)
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_115 = CENTER OF KIEPERT HYPERBOLA (0.6909, 0.0207) X_804 = ODD (- 2, 2) INFINITY POINT (1.1348, 0.3793) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.2977, 0.7013) X_2486 = RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES CIRCLE} (0.6741, 0.0125)
A
B
C
X11
X244
X115
X804
X5
X2783
X2486
Kimberling (6, 9, 13) | AB = 1
X2486 (RADICAL CENTER OF {INCIRCLE, NINE-POINT CIRCLE, MOSES 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 \(f(a,b,c) = bc(b - c)[(b^{2} - c^{2})(a^{2} - bc - ca - ab)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.442022031831\)
▸ Incident Central Lines3 lines
{5 2783 11 244 115 804
▸ Functional Relations4 relations
