X1263
ISOGONAL CONJUGATE OF X1157
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) { 5, 128 }: Central Line L(5, 128) { 4, 195 }: Central Line L(4, 195) { 140, 930 }: Central Line L(140, 930) { 30, 1141 }: Central Line L(30, 1141)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.5871, 1.5280) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_128 = -OF-ORTHIC-TRIANGLE (0.3310, 0.3690) X_4 = ORTHOCENTER (0.6122, 0.3958) X_195 = -CEVA CONJUGATE OF X(3) (0.6761, 0.3331) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_930 = ANTICOMPLEMENT OF X(137) (0.0497, 0.3422) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_1141 = GIBERT POINT (-0.0724, -0.2027) X_1263 = ISOGONAL CONJUGATE OF X(1157) (1.0064, 0.0088)
A
B
C
X1157
X5
X128
X4
X195
X140
X930
X30
X1141
X1263
(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) { 5, 128 }: Central Line L(5, 128) { 4, 195 }: Central Line L(4, 195) { 140, 930 }: Central Line L(140, 930) { 30, 1141 }: Central Line L(30, 1141)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.2743, 0.8850) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_128 = -OF-ORTHIC-TRIANGLE (1.4211, 0.8430) X_4 = ORTHOCENTER (0.6400, 0.4800) X_195 = -CEVA CONJUGATE OF X(3) (0.7800, 0.3200) X_140 = MIDPOINT OF X(3) AND X(5) (0.5350, 0.1200) X_930 = ANTICOMPLEMENT OF X(137) (0.0428, 0.2025) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_1141 = GIBERT POINT (0.0813, -0.0531) X_1263 = ISOGONAL CONJUGATE OF X(1157) (0.7428, 0.3625)
A
B
C
X1157
X5
X128
X4
X195
X140
X930
X30
X1141
X1263
(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) { 5, 128 }: Central Line L(5, 128) { 4, 195 }: Central Line L(4, 195) { 140, 930 }: Central Line L(140, 930) { 30, 1141 }: Central Line L(30, 1141)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (1.2347, 1.0081) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_128 = -OF-ORTHIC-TRIANGLE (0.2641, 0.3398) X_4 = ORTHOCENTER (0.6180, 0.4859) X_195 = -CEVA CONJUGATE OF X(3) (0.7361, 0.3239) X_140 = MIDPOINT OF X(3) AND X(5) (0.5295, 0.1215) X_930 = ANTICOMPLEMENT OF X(137) (0.0736, 0.2611) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_1141 = GIBERT POINT (0.1295, -0.0577) X_1263 = ISOGONAL CONJUGATE OF X(1157) (0.8694, 0.1410)
A
B
C
X1157
X5
X128
X4
X195
X140
X930
X30
X1141
X1263
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) { 5, 128 }: Central Line L(5, 128) { 4, 195 }: Central Line L(4, 195) { 140, 930 }: Central Line L(140, 930) { 30, 1141 }: Central Line L(30, 1141)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X(54) (0.7309, -0.2409) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_128 = -OF-ORTHIC-TRIANGLE (0.4234, 0.0307) X_4 = ORTHOCENTER (0.6331, 0.8294) X_195 = -CEVA CONJUGATE OF X(3) (3.2601, 0.1287) X_140 = MIDPOINT OF X(3) AND X(5) (0.5333, 0.0013) X_930 = ANTICOMPLEMENT OF X(137) (0.2137, -0.7681) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_1141 = GIBERT POINT (-0.5053, -0.0002) X_1263 = ISOGONAL CONJUGATE OF X(1157) (0.8529, 0.7708)
A
B
C
X1157
X5
X128
X4
X195
X140
X930
X30
X1141
X1263
Kimberling (6, 9, 13) | AB = 1
X1263 (ISOGONAL CONJUGATE OF X1157 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\) , where f(a,b,c) is as in
X1157 )
Search Value (6, 9, 13): \(-6.804368895444\)
X1263
▸ Incident Central Lines4 lines
{4 195 5 128 30 1141 140 930
▸ Functional Relations6 relations
Notes
Let A' be the reflection in BC of the A -vertex of the antipedal triangle of X5 B' and C' cyclically. The circumcircles of A'BC , B'CA , and C'AB concur at X1263 Randy Hutson , December 2, 2017)
