X2805
ISOGONAL CONJUGATE OF X2721
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) { 11, 126 }: Central Line L(11, 126) { 37, 100 }: Central Line L(37, 100) { 75, 149 }: Central Line L(75, 149) { 30, 511 }: Central Line L(30, 511) { 104, 1296 }: Central Line L(104, 1296)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2721 = SR(X(100), X(111)) (0.1108, 0.4321) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_126 = -OF-MEDIAL-TRIANGLE (0.3119, 0.3228) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4988, 0.1682) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0115, 0.2498) X_2805 = ISOGONAL CONJUGATE OF X(2721) (0.0355, 0.5040)
A
B
C
X2721
X11
X126
X37
X100
X75
X149
X30
X511
X104
X1296
X2805
(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) { 11, 126 }: Central Line L(11, 126) { 37, 100 }: Central Line L(37, 100) { 75, 149 }: Central Line L(75, 149) { 30, 511 }: Central Line L(30, 511) { 104, 1296 }: Central Line L(104, 1296)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2721 = SR(X(100), X(111)) (0.1506, 0.3576) X_11 = FEUERBACH POINT (0.7200, 0.0400) X_126 = -OF-MEDIAL-TRIANGLE (0.3221, 0.2725) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4826, 0.1226) X_149 = REFLECTION OF X(20) IN X(104) (1.2400, -0.3200) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2569, -0.3367) X_104 = ANTIPODE OF X(100) (0.8000, -0.4000) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0042, 0.0649) X_2805 = ISOGONAL CONJUGATE OF X(2721) (0.0502, 0.4501)
A
B
C
X2721
X11
X126
X37
X100
X75
X149
X30
X511
X104
X1296
X2805
(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) { 11, 126 }: Central Line L(11, 126) { 37, 100 }: Central Line L(37, 100) { 75, 149 }: Central Line L(75, 149) { 30, 511 }: Central Line L(30, 511) { 104, 1296 }: Central Line L(104, 1296)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2721 = SR(X(100), X(111)) (0.0664, 0.2490) X_11 = FEUERBACH POINT (0.6897, 0.0298) X_126 = -OF-MEDIAL-TRIANGLE (0.3179, 0.3089) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4859, 0.1249) X_149 = REFLECTION OF X(20) IN X(104) (1.1407, -0.3666) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2881, -0.3552) X_104 = ANTIPODE OF X(100) (0.7614, -0.4263) X_1296 = COLLINGS TRANSFORM OF X(126) (0.0177, 0.1319) X_2805 = ISOGONAL CONJUGATE OF X(2721) (0.0795, 0.5071)
A
B
C
X2721
X11
X126
X37
X100
X75
X149
X30
X511
X104
X1296
X2805
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) { 11, 126 }: Central Line L(11, 126) { 37, 100 }: Central Line L(37, 100) { 75, 149 }: Central Line L(75, 149) { 30, 511 }: Central Line L(30, 511) { 104, 1296 }: Central Line L(104, 1296)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2721 = SR(X(100), X(111)) (0.0842, 0.1159) X_11 = FEUERBACH POINT (0.6563, 0.0066) X_126 = -OF-MEDIAL-TRIANGLE (0.2869, 0.2211) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_75 = ISOTOMIC CONJUGATE OF INCENTER (0.4506, 0.0607) X_149 = REFLECTION OF X(20) IN X(104) (0.9920, -0.2537) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_511 = ISOGONAL CONJUGATE OF X(98) (0.3235, -0.5244) X_104 = ANTIPODE OF X(100) (0.6794, -0.8162) X_1296 = COLLINGS TRANSFORM OF X(126) (-0.0593, -0.3873) X_2805 = ISOGONAL CONJUGATE OF X(2721) (-0.0230, 0.4228)
A
B
C
X2721
X11
X126
X37
X100
X75
X149
X30
X511
X104
X1296
X2805
Kimberling (6, 9, 13) | AB = 1
X2805 (ISOGONAL CONJUGATE OF X2721 ) 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 at
X2721 Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines5 lines
{11 126 30 511 37 100 75 149 104 1296
▸ Functional Relations1 relation
Notes
Let Ia be the reflection of X1 BC , and define Ib and Ic cyclically. X2805 X524 Ia Ib Ic ; Ia Ib Ic is the inner Garcia triangle. (Randy Hutson , February 10, 2016)
