X263
ISOGONAL CONJUGATE OF X183
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, 51 }: Central Line L(2, 51) { 6, 160 }: Central Line L(6, 160) { 184, 251 }: Central Line L(184, 251) { 69, 308 }: Central Line L(69, 308)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4700, 0.1275) X_2 = CENTROID (0.5374, 0.2000) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6093, 0.3186) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4841, -0.0647) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6177, 0.3042) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4915, 0.1700) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6298, 0.3525)
A
B
C
X183
X2
X51
X6
X160
X184
X251
X69
X308
X263
(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, 51 }: Central Line L(2, 51) { 6, 160 }: Central Line L(6, 160) { 184, 251 }: Central Line L(184, 251) { 69, 308 }: Central Line L(69, 308)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4363, 0.0654) X_2 = CENTROID (0.5467, 0.1600) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6400, 0.3200) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_160 = -OF-TANGENTIAL-TRIANGLE (0.5000, -0.5208) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6400, 0.0000) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6571, 0.2840) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3600, 0.0000) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4655, 0.1249) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6615, 0.3569)
A
B
C
X183
X2
X51
X6
X160
X184
X251
X69
X308
X263
(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, 51 }: Central Line L(2, 51) { 6, 160 }: Central Line L(6, 160) { 184, 251 }: Central Line L(184, 251) { 69, 308 }: Central Line L(69, 308)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.4472, 0.0671) X_2 = CENTROID (0.5393, 0.1620) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6180, 0.3239) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_160 = -OF-TANGENTIAL-TRIANGLE (0.5000, -0.5145) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6180, 0.0000) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6328, 0.2886) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3820, 0.0000) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4721, 0.1282) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6366, 0.3621)
A
B
C
X183
X2
X51
X6
X160
X184
X251
X69
X308
X263
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, 51 }: Central Line L(2, 51) { 6, 160 }: Central Line L(6, 160) { 184, 251 }: Central Line L(184, 251) { 69, 308 }: Central Line L(69, 308)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_183 = TRILINEAR PRODUCT X(75)X(182) (0.3743, -0.0152) X_2 = CENTROID (0.5444, 0.0934) X_51 = CENTROID OF ORTHIC TRIANGLE (0.6126, 0.2841) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_160 = -OF-TANGENTIAL-TRIANGLE (0.4566, 0.9160) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.3215, 1.0549) X_251 = ISOGONAL CONJUGATE OF X(141) (0.6603, 0.2039) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3185, -0.0509) X_308 = ISOTOMIC CONJUGATE OF X(39) (0.4157, 0.0638) X_263 = ISOGONAL CONJUGATE OF X(183) (0.6200, 0.3050)
A
B
C
X183
X2
X51
X6
X160
X184
X251
X69
X308
X263
Kimberling (6, 9, 13) | AB = 1
X263 (ISOGONAL CONJUGATE OF X183 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a^{2}\sec(A - \omega ) : :\)
Barycentrics: \(a^{3}\sec(A - \omega ) : :\)
Search Value (6, 9, 13): \(-0.154184177668\)
▸ Incident Central Lines4 lines
{2 51 6 160 69 308 184 251
▸ Functional Relations2 relations
Notes
Let V = U(2)-of-pedal-triangle-of-P(1), and let W = P(2)-of-pedal-triangle-of-U(1). Then X263 trilinear pole of VW . (Randy Hutson , December 26, 2015)
Let A1 B1 C1 and A2 B2 C2 be the pedal triangles of PU(1). Then X263
