X2025
RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES
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) { 39, 1570 }: Brocard Axis { 3, 6 }: Brocard Axis
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.4005, -0.0623) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2025 = RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES (0.4891, 0.0841)
A
B
C
X39
X1570
X3
X6
X2025
(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) { 39, 1570 }: Brocard Axis { 3, 6 }: Brocard Axis
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_39 = BROCARD MIDPOINT (0.6138, 0.1951) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.5355, 0.0609) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_2025 = RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES (0.5747, 0.1280)
A
B
C
X39
X1570
X3
X6
X2025
(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) { 39, 1570 }: Brocard Axis { 3, 6 }: Brocard Axis
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_39 = BROCARD MIDPOINT (0.5955, 0.1965) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.5225, 0.0464) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_2025 = RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES (0.5590, 0.1215)
A
B
C
X39
X1570
X3
X6
X2025
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) { 39, 1570 }: Brocard Axis { 3, 6 }: Brocard Axis
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_39 = BROCARD MIDPOINT (0.6418, 0.1220) X_1570 = MOSES-CIRCLE INVERSE OF X(3) (0.6317, 0.0937) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_2025 = RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES (0.6367, 0.1078)
A
B
C
X39
X1570
X3
X6
X2025
Kimberling (6, 9, 13) | AB = 1
X2025 (RADICAL TRACE OF GALLATLY AND 2nd LEMOINE CIRCLES ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\cos 2\omega \sin(A + \omega ) - 2 \sin \omega \tan \omega \sin A : :\)
Search Value (6, 9, 13): \(1.750992776207\)
▸ Incident Central Lines1 line
▸ Functional Relations2 relations
