X2563
EXSIMILICENTER(GALLATLY CIRCLE, 2nd BROCARD CIRCLE)
X2563 is the exsimilicenter(gallatly 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 { 2007, 2564 }: Central Line L(2007, 2564) { 2008, 2565 }: Central Line L(2008, 2565) { 2009, 2566 }: Central Line L(2009, 2566) { 2010, 2567 }: Central Line L(2010, 2567) { 2013, 2568 }: Central Line L(2013, 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_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5301, 0.1574) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.3070, -0.2526) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5225, 0.1608) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.3874, -0.1925) X_2013 = INSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.5391, 0.1987) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5121, 0.1503) X_2563 = EXSIMILICENTER(GALLATLY CIRCLE, 2nd BROCARD CIRCLE) (0.3115, -0.2093)
A
B
C
X3
X6
X2007
X2564
X2008
X2565
X2009
X2566
X2010
X2567
X2013
X2568
X2563
(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 { 2007, 2564 }: Central Line L(2007, 2564) { 2008, 2565 }: Central Line L(2008, 2565) { 2009, 2566 }: Central Line L(2009, 2566) { 2010, 2567 }: Central Line L(2010, 2567) { 2013, 2568 }: Central Line L(2013, 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_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.6066, 0.1976) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5556, 0.1112) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.4315, 0.2604) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.9961, 0.9923) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5935, 0.2159) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5350, 0.1201) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.8954, -0.0940) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (36.4916, 123.3999) X_2013 = INSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.5496, 0.1574) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5143, 0.1001) X_2563 = EXSIMILICENTER(GALLATLY CIRCLE, 2nd BROCARD CIRCLE) (1.3353, 1.4319)
A
B
C
X3
X6
X2007
X2564
X2008
X2565
X2009
X2566
X2010
X2567
X2013
X2568
X2563
(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 { 2007, 2564 }: Central Line L(2007, 2564) { 2008, 2565 }: Central Line L(2008, 2565) { 2009, 2566 }: Central Line L(2009, 2566) { 2010, 2567 }: Central Line L(2010, 2567) { 2013, 2568 }: Central Line L(2013, 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_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5896, 0.1994) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5459, 0.1103) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.4433, 0.2705) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (1.0000, 1.2021) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5785, 0.2182) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5291, 0.1197) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.8486, -0.1254) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (-1.5291, -8.3524) X_2013 = INSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.5418, 0.1592) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5120, 0.1002) X_2563 = EXSIMILICENTER(GALLATLY CIRCLE, 2nd BROCARD CIRCLE) (1.4497, 1.9547)
A
B
C
X3
X6
X2007
X2564
X2008
X2565
X2009
X2566
X2010
X2567
X2013
X2568
X2563
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 { 2007, 2564 }: Central Line L(2007, 2564) { 2008, 2565 }: Central Line L(2008, 2565) { 2009, 2566 }: Central Line L(2009, 2566) { 2010, 2567 }: Central Line L(2010, 2567) { 2013, 2568 }: Central Line L(2013, 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_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.6265, 0.1267) X_2564 = INSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.5892, 0.0383) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5456, 0.1511) X_2565 = EXSIMILICENTER(INCIRCLE, 2nd BROCARD CIRCLE) (0.6632, 0.2977) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.6128, 0.1820) X_2566 = INSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.5405, 0.0614) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.7691, -0.1407) X_2567 = EXSIMILICENTER(NINE-POINT CIRCLE, 2nd BROCARD CIRCLE) (0.6863, 1.2707) X_2013 = INSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.5443, 0.0875) X_2568 = INSIMILICENTER(SPIEKER CIRCLE, 2ndBROCARD CIRCLE) (0.5077, 0.0303) X_2563 = EXSIMILICENTER(GALLATLY CIRCLE, 2nd BROCARD CIRCLE) (0.7379, 0.3909)
A
B
C
X3
X6
X2007
X2564
X2008
X2565
X2009
X2566
X2010
X2567
X2013
X2568
X2563
Kimberling (6, 9, 13) | AB = 1
X2563 (EXSIMILICENTER(GALLATLY 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
\(f(A,B,C) = \cos A - e \sin(A + \omega )\) , 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): \(-1.971425426810\)
▸ Incident Central Lines9 lines
{3 6 2007 2564 2008 2565 2009 2566 2010 2567 2013 2568 2014 2569 2017 2572 2018 2573
▸ Functional Relations1 relation
