X1668
EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE)
X1668 is the exsimilicenter(Brocard circle, 2nd Lemoine 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) { 3, 6 }: Brocard Axis { 485, 1348 }: Central Line L(485, 1348) { 486, 1349 }: Central Line L(486, 1349) { 1124, 1674 }: Central Line L(1124, 1674) { 1335, 1675 }: Central Line L(1335, 1675) { 1377, 1678 }: Central Line L(1377, 1678)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_485 = VECTEN POINT (0.5773, 0.2578) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5517, 0.2023) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5563, 0.1989) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5349, 0.1503) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5443, 0.2084) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5366, 0.1840) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.5226, 0.1394)
A
B
C
X3
X6
X485
X1348
X486
X1349
X1124
X1674
X1335
X1675
X1377
X1678
X1668
(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) { 3, 6 }: Brocard Axis { 485, 1348 }: Central Line L(485, 1348) { 486, 1349 }: Central Line L(486, 1349) { 1124, 1674 }: Central Line L(1124, 1674) { 1335, 1675 }: Central Line L(1335, 1675) { 1377, 1678 }: Central Line L(1377, 1678)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_485 = VECTEN POINT (0.6057, 0.2400) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5700, 0.1629) X_486 = INNER VECTEN POINT (2.3200, 0.2400) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5700, -0.0301) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6182, 0.2182) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5823, 0.1528) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4000, 0.0000) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5018, -0.0620) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5553, 0.1694) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5409, 0.1316) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.4738, -0.0449)
A
B
C
X3
X6
X485
X1348
X486
X1349
X1124
X1674
X1335
X1675
X1377
X1678
X1668
(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) { 3, 6 }: Brocard Axis { 485, 1348 }: Central Line L(485, 1348) { 486, 1349 }: Central Line L(486, 1349) { 1124, 1674 }: Central Line L(1124, 1674) { 1335, 1675 }: Central Line L(1335, 1675) { 1377, 1678 }: Central Line L(1377, 1678)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_485 = VECTEN POINT (0.5889, 0.2429) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5590, 0.1641) X_486 = INNER VECTEN POINT (2.6471, 0.2429) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5590, -0.0212) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5995, 0.2206) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5690, 0.1538) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4159, 0.0000) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.5086, -0.0409) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5467, 0.1716) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5350, 0.1331) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.4851, -0.0306)
A
B
C
X3
X6
X485
X1348
X486
X1349
X1124
X1674
X1335
X1675
X1377
X1678
X1668
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) { 3, 6 }: Brocard Axis { 485, 1348 }: Central Line L(485, 1348) { 486, 1349 }: Central Line L(486, 1349) { 1124, 1674 }: Central Line L(1124, 1674) { 1335, 1675 }: Central Line L(1335, 1675) { 1377, 1678 }: Central Line L(1377, 1678)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_485 = VECTEN POINT (0.6212, 0.2100) X_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5732, 0.0949) X_486 = INNER VECTEN POINT (0.8351, -0.0536) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.6336, -1.5605) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6325, 0.1445) X_1674 = INSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.6023, 0.0640) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.5226, 0.0516) X_1675 = EXSIMILICENTER(INCIRCLE, BROCARD CIRCLE) (0.6614, 0.3615) X_1377 = INSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5469, 0.0982) X_1678 = INSIMILICENTER(BROCARD CIRCLE, SPIEKER CIRCLE) (0.5241, 0.0468) X_1668 = EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) (0.9881, 1.0908)
A
B
C
X3
X6
X485
X1348
X486
X1349
X1124
X1674
X1335
X1675
X1377
X1678
X1668
Kimberling (6, 9, 13) | AB = 1
X1668 (EXSIMILICENTER(BROCARD CIRCLE, 2nd LEMOINE CIRCLE) ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\cos(A - \omega ) - e \sin A : :\)
Search Value (6, 9, 13): \(-11.177856555399\)
▸ Linear Combinations2 combinations
▸ Incident Central Lines9 lines
{3 6 485 1348 486 1349 1124 1674 1335 1675 1377 1678 1378 1679 1702 1704 1703 1705
▸ Functional Relations2 relations
