X2502
RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY 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) { 6, 110 }: Central Line L(6, 110) { 2, 353 }: Central Line L(2, 353) { 23, 352 }: Central Line L(23, 352) { 187, 237 }: Central Line L(187, 237) { 694, 1383 }: Central Line L(694, 1383) { 543, 1641 }: Central Line L(543, 1641)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_583 = ORTHOGONAL OF X(500) (0.6638, 0.3726) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_2 = CENTROID (0.5374, 0.2000) X_353 = INVERSE-IN-BROCARD-CIRCLE OF X(111) (0.5667, 0.1759) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_352 = INVERSE-IN-CIRCUMCIRCLE OF X(353) (2.2545, 2.0453) 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_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_1383 = 1st GRINBERG HOMOTHETIC CENTER (0.6286, 0.3456) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (0.0220, 0.4806) X_1641 = TRIPOLAR CENTROID OF X(99) (1.6884, 1.4368) X_2502 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY CIRCLE} (-6.1552, 5.7085)
A
B
C
X583
X6
X110
X2
X353
X23
X352
X187
X237
X694
X1383
X543
X1641
X2502
(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) { 6, 110 }: Central Line L(6, 110) { 2, 353 }: Central Line L(2, 353) { 23, 352 }: Central Line L(23, 352) { 187, 237 }: Central Line L(187, 237) { 694, 1383 }: Central Line L(694, 1383) { 543, 1641 }: Central Line L(543, 1641)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_583 = ORTHOGONAL OF X(500) (0.7117, 0.3630) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_110 = FOCUS OF KIEPERT PARABOLA (0.3600, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_353 = INVERSE-IN-BROCARD-CIRCLE OF X(111) (0.6081, 0.1034) X_23 = FAR-OUT POINT (0.9200, 1.4400) X_352 = INVERSE-IN-CIRCUMCIRCLE OF X(353) (1.7073, 1.1548) 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_694 = ISOGONAL CONJUGATE OF X(385) (1.0176, 0.0462) X_1383 = 1st GRINBERG HOMOTHETIC CENTER (0.6623, 0.3354) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (0.0326, 0.4175) X_1641 = TRIPOLAR CENTROID OF X(99) (1.3299, 0.8313) X_2502 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY CIRCLE} (-1.9896, 2.4939)
A
B
C
X583
X6
X110
X2
X353
X23
X352
X187
X237
X694
X1383
X543
X1641
X2502
(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) { 6, 110 }: Central Line L(6, 110) { 2, 353 }: Central Line L(2, 353) { 23, 352 }: Central Line L(23, 352) { 187, 237 }: Central Line L(187, 237) { 694, 1383 }: Central Line L(694, 1383) { 543, 1641 }: Central Line L(543, 1641)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_583 = ORTHOGONAL OF X(500) (0.6797, 0.3698) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_110 = FOCUS OF KIEPERT PARABOLA (0.3820, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_353 = INVERSE-IN-BROCARD-CIRCLE OF X(111) (0.5907, 0.1025) X_23 = FAR-OUT POINT (0.8541, 1.4576) X_352 = INVERSE-IN-CIRCUMCIRCLE OF X(353) (1.7108, 1.3675) 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_694 = ISOGONAL CONJUGATE OF X(385) (1.0000, 0.0000) X_1383 = 1st GRINBERG HOMOTHETIC CENTER (0.6372, 0.3417) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (0.0602, 0.4798) X_1641 = TRIPOLAR CENTROID OF X(99) (0.9079, 0.5412) X_2502 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY CIRCLE} (-0.7236, 1.6236)
A
B
C
X583
X6
X110
X2
X353
X23
X352
X187
X237
X694
X1383
X543
X1641
X2502
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) { 6, 110 }: Central Line L(6, 110) { 2, 353 }: Central Line L(2, 353) { 23, 352 }: Central Line L(23, 352) { 187, 237 }: Central Line L(187, 237) { 694, 1383 }: Central Line L(694, 1383) { 543, 1641 }: Central Line L(543, 1641)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_583 = ORTHOGONAL OF X(500) (0.6951, 0.2711) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_110 = FOCUS OF KIEPERT PARABOLA (0.4975, 0.2958) X_2 = CENTROID (0.5444, 0.0934) X_353 = INVERSE-IN-BROCARD-CIRCLE OF X(111) (0.6869, -0.0788) X_23 = FAR-OUT POINT (0.6051, 0.5970) X_352 = INVERSE-IN-CIRCUMCIRCLE OF X(353) (1.3299, 0.5949) 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_694 = ISOGONAL CONJUGATE OF X(385) (1.0028, 0.0106) X_1383 = 1st GRINBERG HOMOTHETIC CENTER (0.6472, 0.2490) X_543 = DIRECTION OF VECTOR AX + BX + CX, where X = X(99) (-0.0433, 0.3849) X_1641 = TRIPOLAR CENTROID OF X(99) (0.8066, 0.2608) X_2502 = RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY CIRCLE} (0.1263, 0.5983)
A
B
C
X583
X6
X110
X2
X353
X23
X352
X187
X237
X694
X1383
X543
X1641
X2502
Kimberling (6, 9, 13) | AB = 1
X2502 (RADICAL CENTER OF {CIRCUMCIRCLE, BROCARD CIRCLE, PARRY CIRCLE} ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a(2a^{4} - b^{4} - c^{4} + 4b^{2}c^{2} - 2a^{2}b^{2} - 2a^{2}c^{2})\)
Search Value (6, 9, 13): \(0.709453639030\)
▸ Incident Central Lines7 lines
{2 353 6 110 23 352 187 237 542 1648 543 1641 694 1383
▸ Functional Relations11 relations
