X2485
RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT 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) { 230, 231 }: Central Line L(230, 231) { 6, 520 }: Central Line L(6, 520) { 512, 1691 }: Central Line L(512, 1691) { 2165, 2395 }: Central Line L(2165, 2395) { 525, 2507 }: Central Line L(525, 2507) { 669, 2514 }: Central Line L(669, 2514)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0490, 0.2227) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.9991, 0.9263) X_2165 = -ISOCONJUGATE OF X(47) (-0.1110, -0.0295) X_2395 = GIBERT-SIMSON TRANSFORM OF X(98) (1.0626, 0.0904) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.8163, 0.3364) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (8.7303, -4.2052) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (2.1894, 0.2056)
A
B
C
X230
X231
X6
X520
X512
X1691
X2165
X2395
X525
X2507
X669
X2514
X2485
(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) { 230, 231 }: Central Line L(230, 231) { 6, 520 }: Central Line L(6, 520) { 512, 1691 }: Central Line L(512, 1691) { 2165, 2395 }: Central Line L(2165, 2395) { 525, 2507 }: Central Line L(525, 2507) { 669, 2514 }: Central Line L(669, 2514)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_230 = -CEVA CONJUGATE OF X(114) (0.8489, 0.4191) X_231 = -CEVA CONJUGATE OF X(128) (0.9181, 0.3989) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0283, 0.1600) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.8489, 0.5981) X_2165 = -ISOCONJUGATE OF X(47) (1.4629, 0.2400) X_2395 = GIBERT-SIMSON TRANSFORM OF X(98) (1.0837, 0.1106) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.7941, 0.2400) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-1.2857, 2.0833) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (4.2114, -1.6033) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (1.4629, 0.2400)
A
B
C
X230
X231
X6
X520
X512
X1691
X2165
X2395
X525
X2507
X669
X2514
X2485
(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) { 230, 231 }: Central Line L(230, 231) { 6, 520 }: Central Line L(6, 520) { 512, 1691 }: Central Line L(512, 1691) { 2165, 2395 }: Central Line L(2165, 2395) { 525, 2507 }: Central Line L(525, 2507) { 669, 2514 }: Central Line L(669, 2514)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_230 = -CEVA CONJUGATE OF X(114) (0.8090, 0.4395) X_231 = -CEVA CONJUGATE OF X(128) (0.8795, 0.4223) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.0357, 0.1620) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.8090, 0.6360) X_2165 = -ISOCONJUGATE OF X(47) (1.6180, 0.2429) X_2395 = GIBERT-SIMSON TRANSFORM OF X(98) (1.1459, 0.1147) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.8090, 0.2429) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-1.6180, 2.0582) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (4.8541, -1.5723) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (1.6180, 0.2429)
A
B
C
X230
X231
X6
X520
X512
X1691
X2165
X2395
X525
X2507
X669
X2514
X2485
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) { 230, 231 }: Central Line L(230, 231) { 6, 520 }: Central Line L(6, 520) { 512, 1691 }: Central Line L(512, 1691) { 2165, 2395 }: Central Line L(2165, 2395) { 525, 2507 }: Central Line L(525, 2507) { 669, 2514 }: Central Line L(669, 2514)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_230 = -CEVA CONJUGATE OF X(114) (0.7126, 0.2008) X_231 = -CEVA CONJUGATE OF X(128) (1.0516, 0.1599) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_520 = ISOGONAL CONJUGATE OF X(107) (-0.1112, 0.1181) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_1691 = RADICAL TRACE OF CIRCUMCIRCLE AND 1st LEMOINE CIRCLE (0.7087, 0.3091) X_2165 = -ISOCONJUGATE OF X(47) (2.3598, -1.9328) X_2395 = GIBERT-SIMSON TRANSFORM OF X(98) (1.1899, 0.1013) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_2507 = RADICAL CENTER OF {NINE-POINT CIRCLE, 1st LEMOINE CIRCLE, GALLATLY CIRCLE} (0.7934, 0.1329) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-0.1118, 0.6834) X_2514 = RADICAL CENTER OF {CIRCUMCIRCLE, 2nd LEMOINE CIRCLE, (X(4),2R)} (2.4397, -0.3907) X_2485 = RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE} (1.1640, 0.1464)
A
B
C
X230
X231
X6
X520
X512
X1691
X2165
X2395
X525
X2507
X669
X2514
X2485
Kimberling (6, 9, 13) | AB = 1
X2485 (RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT 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 \(f(a,b,c) = a(b^{2} - c^{2})(b^{4} + c^{4} - a^{4})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.805858208362\)
▸ Incident Central Lines6 lines
{6 520 230 231 512 1691 525 2507 669 2514 2165 2395
▸ Functional Relations14 relations
X2485 i and Xj for these (i,j): (647 2489 669 2514
X2485 i in Xj for these (i,j): (2489 2492 2506 647
X2485 isogonal conjugate of the isotomic conjugate of X33294
X2485 complement of X3267
X2485 X2 X127
X2485 8673
X2485 X63 isoconjugate of X1289
X2485 crosspoint of Xi and Xj for these (i,j): (2 112 83 107
X2485 crosssum of Xi and Xj for these (i,j): (6 525 39 520
X2485 X127 A , B , C ,X4 X22
X2485 trilinear poles of lines passing through X127
X2485 trilinear polars of X4 X22
X2485 crossdifference of every pair of points on line X3 X66
X2485 14580
