X2561
EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE)
X2561 is the exsimilicenter(2nd Lemoine circle, 2nd Brocard 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, 2566 }: Central Line L(485, 2566) { 486, 2567 }: Central Line L(486, 2567) { 1124, 2564 }: Central Line L(1124, 2564) { 1335, 2565 }: Central Line L(1335, 2565) { 1337, 2568 }: Central Line L(1337, 2568)
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_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5225, 0.1608) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.3874, -0.1925) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5301, 0.1574) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.3070, -0.2526) X_1337 = 1st WERNAU POINT (2.6910, 4.6498) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5121, 0.1503) X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.3338, -0.1724)
A
B
C
X3
X6
X485
X2566
X486
X2567
X1124
X2564
X1335
X2565
X1337
X2568
X2561
(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, 2566 }: Central Line L(485, 2566) { 486, 2567 }: Central Line L(486, 2567) { 1124, 2564 }: Central Line L(1124, 2564) { 1335, 2565 }: Central Line L(1335, 2565) { 1337, 2568 }: Central Line L(1337, 2568)
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_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5350, 0.1201) X_486 = INNER VECTEN POINT (2.3200, 0.2400) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (36.4916, 123.3999) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6182, 0.2182) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5556, 0.1112) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4000, 0.0000) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.9961, 0.9923) X_1337 = 1st WERNAU POINT (1.6606, 2.8536) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5143, 0.1001) X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (3.8439, 5.7324)
A
B
C
X3
X6
X485
X2566
X486
X2567
X1124
X2564
X1335
X2565
X1337
X2568
X2561
(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, 2566 }: Central Line L(485, 2566) { 486, 2567 }: Central Line L(486, 2567) { 1124, 2564 }: Central Line L(1124, 2564) { 1335, 2565 }: Central Line L(1335, 2565) { 1337, 2568 }: Central Line L(1337, 2568)
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_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5291, 0.1197) X_486 = INNER VECTEN POINT (2.6471, 0.2429) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (-1.5291, -8.3524) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5995, 0.2206) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5459, 0.1103) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4159, 0.0000) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (1.0000, 1.2021) X_1337 = 1st WERNAU POINT (1.5017, 2.9582) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5120, 0.1002) X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.7906, 0.6791)
A
B
C
X3
X6
X485
X2566
X486
X2567
X1124
X2564
X1335
X2565
X1337
X2568
X2561
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, 2566 }: Central Line L(485, 2566) { 486, 2567 }: Central Line L(486, 2567) { 1124, 2564 }: Central Line L(1124, 2564) { 1335, 2565 }: Central Line L(1335, 2565) { 1337, 2568 }: Central Line L(1337, 2568)
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_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5405, 0.0614) X_486 = INNER VECTEN POINT (0.8351, -0.0536) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.6863, 1.2707) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6325, 0.1445) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5892, 0.0383) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.5226, 0.0516) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.6632, 0.2977) X_1337 = 1st WERNAU POINT (0.7818, 1.4449) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5077, 0.0303) X_2561 = EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.7739, 0.4915)
A
B
C
X3
X6
X485
X2566
X486
X2567
X1124
X2564
X1335
X2565
X1337
X2568
X2561
Kimberling (6, 9, 13) | AB = 1
X2561 (EXSIMILICENTER(2nd LEMOINE CIRCLE, 2nd BROCARD 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
\(f(A,B,C) = \cos A - e \sin A\) , e as at
X2556 Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-3.294614822454\)
▸ Incident Central Lines9 lines
{3 6 485 2566 486 2567 1124 2564 1335 2565 1337 2568 1378 2569 1702 2572 1703 2573
▸ Functional Relations2 relations
X2561 X2560
X2561 X2556
