X2080
INVERSE-IN-CIRCUMCIRCLE OF X182
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) circumcircle: Circumcircle of △ABC { 3, 182 }: Brocard Axis { 3, 6 }: Brocard Axis { 30, 98 }: Central Line L(30, 98) { 83, 140 }: Central Line L(83, 140) { 5, 316 }: Central Line L(5, 316)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_98 = TARRY POINT (0.8891, -0.2281) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5651, 0.2360) X_140 = MIDPOINT OF X(3) AND X(5) (0.5281, 0.1755) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_316 = DROUSSENT PIVOT (-0.7850, -1.9118) X_2080 = INVERSE-IN-CIRCUMCIRCLE OF X(182) (1.8972, 2.4097)
A
B
C
X3
X182
X6
X30
X98
X83
X140
X5
X316
X2080
(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) circumcircle: Circumcircle of △ABC { 3, 182 }: Brocard Axis { 3, 6 }: Brocard Axis { 30, 98 }: Central Line L(30, 98) { 83, 140 }: Central Line L(83, 140) { 5, 316 }: Central Line L(5, 316)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5700, 0.1200) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_98 = TARRY POINT (0.8489, -0.3581) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5865, 0.2047) X_140 = MIDPOINT OF X(3) AND X(5) (0.5350, 0.1200) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_316 = DROUSSENT PIVOT (-0.2667, -1.0744) X_2080 = INVERSE-IN-CIRCUMCIRCLE OF X(182) (1.4067, 1.5544)
A
B
C
X3
X182
X6
X30
X98
X83
X140
X5
X316
X2080
(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) circumcircle: Circumcircle of △ABC { 3, 182 }: Brocard Axis { 3, 6 }: Brocard Axis { 30, 98 }: Central Line L(30, 98) { 83, 140 }: Central Line L(83, 140) { 5, 316 }: Central Line L(5, 316)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5590, 0.1215) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_98 = TARRY POINT (0.8090, -0.3931) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5729, 0.2075) X_140 = MIDPOINT OF X(3) AND X(5) (0.5295, 0.1215) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_316 = DROUSSENT PIVOT (-0.1910, -1.1792) X_2080 = INVERSE-IN-CIRCUMCIRCLE OF X(182) (1.3090, 1.6651)
A
B
C
X3
X182
X6
X30
X98
X83
X140
X5
X316
X2080
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) circumcircle: Circumcircle of △ABC { 3, 182 }: Brocard Axis { 3, 6 }: Brocard Axis { 30, 98 }: Central Line L(30, 98) { 83, 140 }: Central Line L(83, 140) { 5, 316 }: Central Line L(5, 316)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5787, -0.0546) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_98 = TARRY POINT (0.7487, -0.7881) X_83 = CEVAPOINT OF CENTROID AND SYMMEDIAN POINT (0.5905, 0.1374) X_140 = MIDPOINT OF X(3) AND X(5) (0.5333, 0.0013) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_316 = DROUSSENT PIVOT (0.1644, -0.4818) X_2080 = INVERSE-IN-CIRCUMCIRCLE OF X(182) (0.9687, 1.0365)
A
B
C
X3
X182
X6
X30
X98
X83
X140
X5
X316
X2080
Kimberling (6, 9, 13) | AB = 1
X2080 (INVERSE-IN-CIRCUMCIRCLE OF X182 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(2 \cos A - \cos(A - 2\omega ) : :\)
Search Value (6, 9, 13): \(-10.464130369380\)
▸ Incident Central Lines7 lines
{3 6 5 316 30 98 83 140 110 237 114 754 625 1656
▸ Functional Relations12 relations
Notes
The locus of X23 ABC ) is a circle with center X2080 X23 X385 11676 . This circle is the reflection of the circumcircle in X187 Randy Hutson , August 29, 2018)
