X2012
EXSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE)
X2012 is the exsimilicenter(gallatly circle, 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 { 1348, 2009 }: Central Line L(1348, 2009) { 1349, 2010 }: Central Line L(1349, 2010)
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_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5517, 0.2023) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5673, 0.2394) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5463, 0.1455) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.9341, -0.0718) X_2012 = EXSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE) (0.5314, 0.1539)
A
B
C
X3
X6
X1348
X2009
X1349
X2010
X2012
(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 { 1348, 2009 }: Central Line L(1348, 2009) { 1349, 2010 }: Central Line L(1349, 2010)
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_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5700, 0.1629) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5935, 0.2159) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5700, -0.0301) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.8954, -0.0940) X_2012 = EXSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE) (0.4915, -0.0147)
A
B
C
X3
X6
X1348
X2009
X1349
X2010
X2012
(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 { 1348, 2009 }: Central Line L(1348, 2009) { 2, 3 }: Euler Line { 1349, 2010 }: Central Line L(1349, 2010)
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_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5590, 0.1641) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.5785, 0.2182) X_2 = CENTROID (0.5393, 0.1620) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5590, -0.0212) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.8486, -0.1254) X_2012 = EXSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE) (0.5000, 0.0000)
A
B
C
X3
X6
X1348
X2009
X2
X1349
X2010
X2012
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 { 1348, 2009 }: Central Line L(1348, 2009) { 1349, 2010 }: Central Line L(1349, 2010)
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_1348 = INSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.5732, 0.0949) X_2009 = INSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.6128, 0.1820) X_1349 = EXSIMILICENTER(NINE-POINT CIRCLE, BROCARD CIRCLE) (0.6336, -1.5605) X_2010 = EXSIMILICENTER(GALLATLY CIRCLE, NINE-POINT CIRCLE) (0.7691, -0.1407) X_2012 = EXSIMILICENTER(GALLATLY CIRCLE, BROCARD CIRCLE) (0.8496, 0.7033)
A
B
C
X3
X6
X1348
X2009
X1349
X2010
X2012
Kimberling (6, 9, 13) | AB = 1
X2012 (EXSIMILICENTER(GALLATLY CIRCLE, 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 \(f(A,B,C) = \cos(A - \omega ) - e \sin(A + \omega )\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(-6.080539280518\)
▸ Incident Central Lines3 lines
