X2559
EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE)
X2559 is the exsimilicenter(1st 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 { 1672, 2564 }: Central Line L(1672, 2564) { 1673, 2565 }: Central Line L(1673, 2565) { 1676, 2566 }: Central Line L(1676, 2566) { 1677, 2567 }: Central Line L(1677, 2567) { 1680, 2568 }: Central Line L(1680, 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_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5301, 0.1574) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.3070, -0.2526) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5533, 0.2188) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5225, 0.1608) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.6019, 0.7290) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.3874, -0.1925) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5121, 0.1503) X_2559 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.4285, -0.0161)
A
B
C
X3
X6
X1672
X2564
X1673
X2565
X1676
X2566
X1677
X2567
X1680
X2568
X2559
(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 { 1672, 2564 }: Central Line L(1672, 2564) { 1673, 2565 }: Central Line L(1673, 2565) { 1676, 2566 }: Central Line L(1676, 2566) { 1677, 2567 }: Central Line L(1677, 2567) { 1680, 2568 }: Central Line L(1680, 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_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5874, 0.1665) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5556, 0.1112) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6776, 0.4070) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.9961, 0.9923) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5700, 0.1831) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5350, 0.1201) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5700, 1.3386) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (36.4916, 123.3999) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5333, 0.1347) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5143, 0.1001) X_2559 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (-0.1537, -1.1207)
A
B
C
X3
X6
X1672
X2564
X1673
X2565
X1676
X2566
X1677
X2567
X1680
X2568
X2559
(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 { 1672, 2564 }: Central Line L(1672, 2564) { 1673, 2565 }: Central Line L(1673, 2565) { 1676, 2566 }: Central Line L(1676, 2566) { 1677, 2567 }: Central Line L(1677, 2567) { 1680, 2568 }: Central Line L(1680, 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_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5735, 0.1681) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5459, 0.1103) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6508, 0.4169) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (1.0000, 1.2021) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5590, 0.1854) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5291, 0.1197) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5590, 1.3295) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (-1.5291, -8.3524) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5282, 0.1364) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5120, 0.1002) X_2559 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.0905, -0.8428)
A
B
C
X3
X6
X1672
X2564
X1673
X2565
X1676
X2566
X1677
X2567
X1680
X2568
X2559
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 { 1672, 2564 }: Central Line L(1672, 2564) { 1673, 2565 }: Central Line L(1673, 2565) { 1676, 2566 }: Central Line L(1676, 2566) { 1677, 2567 }: Central Line L(1677, 2567) { 1680, 2568 }: Central Line L(1680, 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_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6043, 0.0743) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5892, 0.0383) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6434, 0.2709) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.6632, 0.2977) X_1676 = INSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.5725, 0.1157) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5405, 0.0614) X_1677 = EXSIMILICENTER(1st LEMOINE CIRCLE, NINE-POINT CIRCLE) (0.3397, 6.4999) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.6863, 1.2707) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5213, 0.0520) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5077, 0.0303) X_2559 = EXSIMILICENTER(1st LEMOINE CIRCLE, 2nd BROCARD CIRCLE) (0.7436, 0.4068)
A
B
C
X3
X6
X1672
X2564
X1673
X2565
X1676
X2566
X1677
X2567
X1680
X2568
X2559
Kimberling (6, 9, 13) | AB = 1
X2559 (EXSIMILICENTER(1st 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
\(f(A,B,C) = \cos A - e \cos(A - \omega )\) , 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): \(-2.181423278301\)
▸ Incident Central Lines9 lines
{3 6 1672 2564 1673 2565 1676 2566 1677 2567 1680 2568 1681 2569 1700 2572 1701 2573
▸ Functional Relations2 relations
