X2977
RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE}
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) { 100, 190 }: Central Line L(100, 190) { 230, 231 }: Central Line L(230, 231)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_2977 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE} (0.5255, 0.8415)
A
B
C
X100
X190
X230
X231
X2977
(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) { 100, 190 }: Central Line L(100, 190) { 230, 231 }: Central Line L(230, 231)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_190 = YFF PARABOLIC POINT (0.0933, 0.3200) X_230 = -CEVA CONJUGATE OF X(114) (0.8489, 0.4191) X_231 = -CEVA CONJUGATE OF X(128) (0.9181, 0.3989) X_2977 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE} (0.4000, 0.5500)
A
B
C
X100
X190
X230
X231
X2977
(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) { 100, 190 }: Central Line L(100, 190) { 230, 231 }: Central Line L(230, 231)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_190 = YFF PARABOLIC POINT (0.1322, 0.3610) X_230 = -CEVA CONJUGATE OF X(114) (0.8090, 0.4395) X_231 = -CEVA CONJUGATE OF X(128) (0.8795, 0.4223) X_2977 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE} (0.4159, 0.5350)
A
B
C
X100
X190
X230
X231
X2977
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) { 100, 190 }: Central Line L(100, 190) { 230, 231 }: Central Line L(230, 231)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_190 = YFF PARABOLIC POINT (0.1548, 0.2119) X_230 = -CEVA CONJUGATE OF X(114) (0.7126, 0.2008) X_231 = -CEVA CONJUGATE OF X(128) (1.0516, 0.1599) X_2977 = RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE} (0.2790, 0.2531)
A
B
C
X100
X190
X230
X231
X2977
Kimberling (6, 9, 13) | AB = 1
X2977 (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT CIRCLE, AC-INCIRCLE} ) 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 \(f(a,b,c) = bc[(a - b)^{2}(c^{2} + a^{2} - b^{2}) - (a - c)^{2}(a^{2} + b^{2} - c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(3.072068640204\)
▸ Incident Central Lines2 lines
▸ Functional Relations1 relation
Notes
See X2975 AC -incircle.”
