X2457
RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} 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) { 523, 656 }: Central Line L(523, 656) { 650, 2529 }: Central Line L(650, 2529)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (7.5714, -0.8554) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (13.7143, -4.1991) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-51.1684, 24.8198) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (-1.5941, 2.6476)
A
B
C
X523
X656
X650
X2529
X2457
(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) { 523, 656 }: Central Line L(523, 656) { 650, 2529 }: Central Line L(650, 2529)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0987, -0.0010) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (4.0000, 0.0000) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (6.4000, -1.2000) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-21.6800, 9.2400) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.1600, 1.1200)
A
B
C
X523
X656
X650
X2529
X2457
(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) { 523, 656 }: Central Line L(523, 656) { 650, 2529 }: Central Line L(650, 2529)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0981, 0.0262) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (4.6762, 0.0000) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (7.5663, -1.2021) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-25.9916, 9.1808) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.0441, 1.1253)
A
B
C
X523
X656
X650
X2529
X2457
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) { 523, 656 }: Central Line L(523, 656) { 650, 2529 }: Central Line L(650, 2529)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_523 = ISOGONAL CONJUGATE OF X(110) (1.1957, 0.0148) X_656 = CROSSDIFFERENCE OF X(1) AND X(19) (2.5463, 0.1294) X_650 = CROSSDIFFERENCE OF X(1) AND X(3) (3.4560, -0.1300) X_2529 = RADICAL CENTER OF {ORTHOCENTROIDAL, SPIEKER, BEVAN} CIRCLES (-10.0415, 2.2854) X_2457 = RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES (0.8916, 0.3289)
A
B
C
X523
X656
X650
X2529
X2457
Kimberling (6, 9, 13) | AB = 1
X2457 (RADICAL CENTER OF {ORTHOCENTROIDAL, BEVAN, FUHRMANN} CIRCLES ) 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 \(f(a,b,c) = bc(b^{2} - c^{2})[2a^{3} + a^{2}(b + c) - (b + c)(b - c)^{2} - 2a(b^{2} - bc + c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(-2.543767378933\)
▸ Incident Central Lines2 lines
