X2512
RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X4 ,2R)}
The circle (
X4 ,2R) is identified at
X2474 .
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) { 325, 523 }: Central Line L(325, 523) { 512, 650 }: Central Line L(512, 650)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2512 = RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X(4),2R)} (22.2720, -9.3807)
A
B
C
X325
X523
X512
X650
X2512
(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) { 325, 523 }: Central Line L(325, 523) { 512, 650 }: Central Line L(512, 650)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_325 = -HIRST INVERSE OF X(69) (-0.0578, -0.3581) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0987, -0.0010) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (6.4000, -1.2000) X_2512 = RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X(4),2R)} (9.9714, -3.2833)
A
B
C
X325
X523
X512
X650
X2512
(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) { 325, 523 }: Central Line L(325, 523) { 512, 650 }: Central Line L(512, 650)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_325 = -HIRST INVERSE OF X(69) (0.0000, -0.3931) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0981, 0.0262) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (7.5663, -1.2021) X_2512 = RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X(4),2R)} (11.8023, -3.2603)
A
B
C
X325
X523
X512
X650
X2512
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) { 325, 523 }: Central Line L(325, 523) { 512, 650 }: Central Line L(512, 650)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_325 = -HIRST INVERSE OF X(69) (0.2079, -0.1215) X_523 = ISOGONAL CONJUGATE OF X(110) (1.1957, 0.0148) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (3.4560, -0.1300) X_2512 = RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X(4),2R)} (5.0737, -0.7083)
A
B
C
X325
X523
X512
X650
X2512
Kimberling (6, 9, 13) | AB = 1
X2512 (RADICAL CENTER OF {CIRCUMCIRCLE, APOLLONIUS CIRCLE, (X4 ,2R)} ) 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 \(f(a,b,c) = (b^{2} - c^{2})[2a(b^{2} + c^{2}) + bc(a + b + c)]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-24.814915100239\)
▸ Incident Central Lines2 lines
▸ Functional Relations1 relation
