X2520
RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR 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) { 460, 512 }: Central Line L(460, 512) { 513, 676 }: Central Line L(513, 676)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_460 = POINT ANTARES (0.6881, 0.5944) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2449, 0.5665) X_2520 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR CIRCLE} (-3.8122, 3.3193)
A
B
C
X460
X512
X513
X676
X2520
(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) { 460, 512 }: Central Line L(460, 512) { 513, 676 }: Central Line L(513, 676)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_460 = POINT ANTARES (0.6400, 0.4800) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.1200, 0.3400) X_2520 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR CIRCLE} (-0.5600, 1.1800)
A
B
C
X460
X512
X513
X676
X2520
(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) { 460, 512 }: Central Line L(460, 512) { 513, 676 }: Central Line L(513, 676)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_460 = POINT ANTARES (0.6180, 0.4859) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.2021, 0.3440) X_2520 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR CIRCLE} (-0.8270, 1.1880)
A
B
C
X460
X512
X513
X676
X2520
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) { 460, 512 }: Central Line L(460, 512) { 513, 676 }: Central Line L(513, 676)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_460 = POINT ANTARES (0.5733, 0.3332) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_676 = CROSSDIFFERENCE OF X(3) AND X(101) (1.1010, 0.1540) X_2520 = RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR CIRCLE} (0.9713, 0.1910)
A
B
C
X460
X512
X513
X676
X2520
Kimberling (6, 9, 13) | AB = 1
X2520 (RADICAL CENTER OF {CIRCUMCIRCLE, INCIRCLE, TAYLOR 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 \(f(a,b,c) = (b - c)(b + c - a)[a^{3} - (b + c) (b - c)^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-1.746491603314\)
▸ Incident Central Lines2 lines
