X2484
RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN 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) { 44, 513 }: Central Line L(44, 513) { 6, 834 }: Central Line L(6, 834) { 512, 1692 }: Central Line L(512, 1692) { 663, 1919 }: Central Line L(663, 1919)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_834 = ODD (2, 3) INFINITY POINT (1.0367, -0.1085) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7995, 0.5968) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (8.6667, -3.2660) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-2.5853, 3.3187) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-35.7273, 22.7135)
A
B
C
X44
X513
X6
X834
X512
X1692
X663
X1919
X2484
(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) { 44, 513 }: Central Line L(44, 513) { 6, 834 }: Central Line L(6, 834) { 512, 1692 }: Central Line L(512, 1692) { 663, 1919 }: Central Line L(663, 1919)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_834 = ODD (2, 3) INFINITY POINT (1.0397, -0.1358) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7445, 0.4191) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (4.0000, -1.0000) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-0.5773, 1.5464) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-13.7600, 8.8800)
A
B
C
X44
X513
X6
X834
X512
X1692
X663
X1919
X2484
(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) { 44, 513 }: Central Line L(44, 513) { 6, 834 }: Central Line L(6, 834) { 512, 1692 }: Central Line L(512, 1692) { 663, 1919 }: Central Line L(663, 1919)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_834 = ODD (2, 3) INFINITY POINT (1.0536, -0.0952) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.7135, 0.4395) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (4.6762, -1.0000) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (-0.7862, 1.5291) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-16.5727, 8.8383)
A
B
C
X44
X513
X6
X834
X512
X1692
X663
X1919
X2484
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) { 44, 513 }: Central Line L(44, 513) { 6, 834 }: Central Line L(6, 834) { 512, 1692 }: Central Line L(512, 1692) { 663, 1919 }: Central Line L(663, 1919)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_834 = ODD (2, 3) INFINITY POINT (1.1594, -0.1350) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_1692 = RADICAL TRACE OF CIRCUMCIRCLE AND 2nd LEMOINE CIRCLE (0.6830, 0.2373) X_663 = CROSSDIFFERENCE OF X(2) AND X(7) (2.1378, -0.1207) X_1919 = BICENTRIC DIFFERENCE OF PU(12) (0.1852, 0.5339) X_2484 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN CIRCLE} (-5.1673, 2.3286)
A
B
C
X44
X513
X6
X834
X512
X1692
X663
X1919
X2484
Kimberling (6, 9, 13) | AB = 1
X2484 (RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, BEVAN 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 \(f(a,b,c) = a(b - c)(a^{2} + b^{2} + c^{2} + 2bc)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(24.586305592102\)
▸ Incident Central Lines4 lines
▸ Functional Relations5 relations
X2484 i in Xj for these (i,j): (649 2483 2483 2515
X2484 isogonal conjugate of X37215
X2484 crosssum of Xi and Xj for these {i,j}: {1 2484 514 649 2522
X2484 crosspoint of Xi and Xj for these {i,j}: {1 101 2258
X2484 X1 X69
