X2532
RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} 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) { 514, 2487 }: Central Line L(514, 2487) { 513, 2500 }: Central Line L(513, 2500)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0761, -0.0329) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-3.9847, 4.4241) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_2500 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, APOLLONIUS CIRCLE} (6.5340, 0.1485) X_2532 = RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} CIRCLES (8.9543, -1.1690)
A
B
C
X514
X2487
X513
X2500
X2532
(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) { 514, 2487 }: Central Line L(514, 2487) { 513, 2500 }: Central Line L(513, 2500)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0889, -0.0314) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-0.9400, 1.9200) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_2500 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, APOLLONIUS CIRCLE} (3.4811, 0.5027) X_2532 = RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} CIRCLES (4.4541, 0.0162)
A
B
C
X514
X2487
X513
X2500
X2532
(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) { 514, 2487 }: Central Line L(514, 2487) { 513, 2500 }: Central Line L(513, 2500)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_514 = ISOGONAL CONJUGATE OF X(101) (1.0910, -0.0001) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (-1.2371, 1.9090) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_2500 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, APOLLONIUS CIRCLE} (4.0894, 0.4872) X_2532 = RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} CIRCLES (5.2584, 0.0010)
A
B
C
X514
X2487
X513
X2500
X2532
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) { 514, 2487 }: Central Line L(514, 2487) { 513, 2500 }: Central Line L(513, 2500)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_514 = ISOGONAL CONJUGATE OF X(101) (1.1917, -0.0133) X_2487 = RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} (0.2508, 0.5901) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_2500 = RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, APOLLONIUS CIRCLE} (2.2077, 0.3162) X_2532 = RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} CIRCLES (2.6101, 0.2015)
A
B
C
X514
X2487
X513
X2500
X2532
Kimberling (6, 9, 13) | AB = 1
X2532 (RADICAL CENTER OF {APOLLONIUS, SPIEKER, BEVAN} CIRCLES ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Constructed Elements
Central Lines: {514, 2487} , {513, 2500}
Related Centers: X514 (ISOGONAL CONJUGATE OF X101 X2487 (RADICAL CENTER OF {INCIRCLE, SPIEKER CIRCLE, BEVAN CIRCLE} X513 (ISOGONAL CONJUGATE OF X100 X2500 (RADICAL CENTER OF {CIRCUMCIRCLE, SPIEKER CIRCLE, APOLLONIUS CIRCLE}
Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) , where \(f(a,b,c) = (b - c)[5(b + c)a^{3} + 2(b^{2} - bc + c^{2})a^{2} - 3(b + c)(b^{2} + c^{2})a - 4bc(b + c)^{2}]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-14.782913645208\)
▸ Incident Central Lines2 lines
