X2978
RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY 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) { 187, 237 }: Central Line L(187, 237) { 320, 350 }: Central Line L(320, 350) { 661, 788 }: Central Line L(661, 788) { 659, 834 }: Central Line L(659, 834)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_785 = o-(- 3, - 2) CIRCUMCIRCLE POINT (0.2590, 0.5519) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_237 = -LINE CONJUGATE OF X(2) (0.9894, 1.3825) X_320 = ISOTOMIC CONJUGATE OF X(80) (-2.6735, -3.5993) X_350 = -HIRST INVERSE OF X(75) (-3.5227, -3.1370) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (48.4286, -23.0952) X_788 = ODD (- 3, 0) INFINITY POINT (1.0251, -0.1264) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.9286, 2.2162) X_834 = ODD (2, 3) INFINITY POINT (1.0367, -0.1085) X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE} (115.0429, -67.6759)
A
B
C
X785
X6
X187
X237
X320
X350
X661
X788
X659
X834
X2978
(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) { 187, 237 }: Central Line L(187, 237) { 320, 350 }: Central Line L(320, 350) { 661, 788 }: Central Line L(661, 788) { 659, 834 }: Central Line L(659, 834)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_785 = o-(- 3, - 2) CIRCUMCIRCLE POINT (0.3697, 0.4827) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.9534, 0.7772) X_237 = -LINE CONJUGATE OF X(2) (0.7596, 0.8902) X_320 = ISOTOMIC CONJUGATE OF X(80) (-1.5600, -1.9200) X_350 = -HIRST INVERSE OF X(75) (-2.3437, -1.5282) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (20.8000, -8.4000) X_788 = ODD (- 3, 0) INFINITY POINT (1.0243, -0.1601) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.4000, 1.3000) X_834 = ODD (2, 3) INFINITY POINT (1.0397, -0.1358) X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE} (48.4000, -26.9000)
A
B
C
X785
X6
X187
X237
X320
X350
X661
X788
X659
X834
X2978
(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) { 187, 237 }: Central Line L(187, 237) { 320, 350 }: Central Line L(320, 350) { 661, 788 }: Central Line L(661, 788) { 659, 834 }: Central Line L(659, 834)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_785 = o-(- 3, - 2) CIRCUMCIRCLE POINT (0.3903, 0.4878) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.9045, 0.8325) X_237 = -LINE CONJUGATE OF X(2) (0.7236, 0.9204) X_320 = ISOTOMIC CONJUGATE OF X(80) (-1.4042, -2.1471) X_350 = -HIRST INVERSE OF X(75) (-2.2720, -1.7862) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (24.7569, -8.3524) X_788 = ODD (- 3, 0) INFINITY POINT (1.0411, -0.1189) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.6180, 1.2720) X_834 = ODD (2, 3) INFINITY POINT (1.0536, -0.0952) X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE} (57.2483, -26.5431)
A
B
C
X785
X6
X187
X237
X320
X350
X661
X788
X659
X834
X2978
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) { 187, 237 }: Central Line L(187, 237) { 320, 350 }: Central Line L(320, 350) { 661, 788 }: Central Line L(661, 788) { 659, 834 }: Central Line L(659, 834)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_785 = o-(- 3, - 2) CIRCUMCIRCLE POINT (0.5054, 0.2958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (0.7344, 0.3809) X_237 = -LINE CONJUGATE OF X(2) (0.5855, 0.4342) X_320 = ISOTOMIC CONJUGATE OF X(80) (-0.5706, -0.8023) X_350 = -HIRST INVERSE OF X(75) (-1.3735, -0.5734) X_661 = CROSSDIFFERENCE OF X(1) AND X(21) (9.8407, -1.9504) X_788 = ODD (- 3, 0) INFINITY POINT (1.1466, -0.1668) X_659 = CROSSDIFFERENCE OF X(1) AND X(39) (1.1270, 0.5340) X_834 = ODD (2, 3) INFINITY POINT (1.1594, -0.1350) X_2978 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY CIRCLE} (22.2299, -7.3030)
A
B
C
X785
X6
X187
X237
X320
X350
X661
X788
X659
X834
X2978
Kimberling (6, 9, 13) | AB = 1
X2978 (RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, CONWAY 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 \(f(a,b,c) = a[(a + c)b^{3} - (a + b)c^{3}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-91.999013574551\)
▸ Incident Central Lines4 lines
▸ Functional Relations3 relations
