X1799
INVERSE MIMOSA TRANSFORM OF X75
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) { 2, 32 }: Central Line L(2, 32) { 22, 76 }: Central Line L(22, 76) { 25, 183 }: Central Line L(25, 183) { 69, 184 }: Central Line L(69, 184) { 3, 305 }: Central Line L(3, 305) { 95, 325 }: Central Line L(95, 325)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1843 = ZOSMA TRANSFORM OF X(75) (0.6278, 0.4214) X_2 = CENTROID (0.5374, 0.2000) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_22 = EXETER POINT (0.4143, -0.1221) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6329, 0.4497) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5172, 0.1562) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.4477, 0.0833)
A
B
C
X1843
X2
X32
X22
X76
X25
X183
X69
X184
X3
X305
X95
X325
X1799
(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) { 2, 32 }: Central Line L(2, 32) { 22, 76 }: Central Line L(22, 76) { 25, 183 }: Central Line L(25, 183) { 69, 184 }: Central Line L(69, 184) { 3, 305 }: Central Line L(3, 305) { 95, 325 }: Central Line L(95, 325)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1843 = ZOSMA TRANSFORM OF X(75) (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_32 = 3rd POWER POINT (0.6819, 0.3119) X_22 = EXETER POINT (0.3600, -0.4800) X_76 = 3rd BROCARD POINT (0.4124, 0.0899) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6400, 0.4800) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4363, 0.0654) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3600, 0.0000) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6400, 0.0000) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.2404, 0.0000) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5280, 0.0960) X_325 = -HIRST INVERSE OF X(69) (-0.0578, -0.3581) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.4042, 0.0000)
A
B
C
X1843
X2
X32
X22
X76
X25
X183
X69
X184
X3
X305
X95
X325
X1799
(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) { 2, 32 }: Central Line L(2, 32) { 22, 76 }: Central Line L(22, 76) { 25, 183 }: Central Line L(25, 183) { 69, 184 }: Central Line L(69, 184) { 3, 305 }: Central Line L(3, 305) { 95, 325 }: Central Line L(95, 325)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1843 = ZOSMA TRANSFORM OF X(75) (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_32 = 3rd POWER POINT (0.6545, 0.3180) X_22 = EXETER POINT (0.3820, -0.4859) X_76 = 3rd BROCARD POINT (0.4271, 0.0928) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6180, 0.4859) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4472, 0.0671) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3820, 0.0000) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6180, 0.0000) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.2764, 0.0000) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (0.5236, 0.0972) X_325 = -HIRST INVERSE OF X(69) (0.0000, -0.3931) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.4198, 0.0000)
A
B
C
X1843
X2
X32
X22
X76
X25
X183
X69
X184
X3
X305
X95
X325
X1799
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) { 2, 32 }: Central Line L(2, 32) { 22, 76 }: Central Line L(22, 76) { 25, 183 }: Central Line L(25, 183) { 69, 184 }: Central Line L(69, 184) { 3, 305 }: Central Line L(3, 305) { 95, 325 }: Central Line L(95, 325)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1843 = ZOSMA TRANSFORM OF X(75) (0.5230, 0.5213) X_2 = CENTROID (0.5444, 0.0934) X_32 = 3rd POWER POINT (0.6767, 0.2196) X_22 = EXETER POINT (0.8328, 2.4854) X_76 = 3rd BROCARD POINT (0.3495, 0.0360) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.5783, 0.3748) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.3743, -0.0152) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3185, -0.0509) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.3215, 1.0549) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.1864, -0.0120) X_95 = CEVAPOINT OF CENTROID AND CIRCUMCENTER (12.6715, -0.2255) X_325 = -HIRST INVERSE OF X(69) (0.2079, -0.1215) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.3183, -0.1225)
A
B
C
X1843
X2
X32
X22
X76
X25
X183
X69
X184
X3
X305
X95
X325
X1799
Kimberling (6, 9, 13) | AB = 1
X1799 (INVERSE MIMOSA TRANSFORM OF X75 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: (cos A)/(y + z),
\(x : y : z\) =
X75 Barycentrics: \((b^{2} + c^{2} - a^{2})/(b^{2} + c^{2}) : :\)
Search Value (6, 9, 13): \(6.643049806998\)
▸ Alternate Coordinates1 form
▸ Incident Central Lines10 lines
{2 32 3 305 22 76 25 183 69 184 95 325 98 689 287 343 385 1194 1402 1441
▸ Functional Relations8 relations
Notes
Let Cma Cmb Cmc be the circummedial triangle (the circumcevian triangle of X2 A″ be the cevapoint of Cmb and Cmc , and define B″ and C″ cyclically. AA″ , BB″ , and CC″ concur in X1799 Randy Hutson , December 10, 2016)
