X2804
ISOGONAL CONJUGATE OF X2720
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, 123 }: Central Line L(11, 123) { 100, 108 }: Central Line L(100, 108) { 30, 511 }: Central Line L(30, 511) { 104, 1295 }: Central Line L(104, 1295) { 1317, 1359 }: Central Line L(1317, 1359) { 1145, 1769 }: Central Line L(1145, 1769)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2720 = SR(X(100), X(108)) (0.9103, 0.4054) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_123 = -OF-MEDIAL-TRIANGLE (0.5401, -0.0057) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.5320, 0.6114) 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_1295 = COLLINGS TRANSFORM OF X(123) (0.4680, -0.4072) X_1317 = REFLECTION OF X(11) IN X(1) (0.4082, 0.3999) X_1359 = BRISSE TRANSFORM OF X(102) (0.5861, 0.4661) X_1145 = 3rd EHRMANN POINT (0.3061, 0.2999) X_1769 = MIMOSA TRANSFORM OF X(901) (1.3810, 0.6999) X_2804 = ISOGONAL CONJUGATE OF X(2720) (-0.0126, -0.0047)
A
B
C
X2720
X11
X123
X100
X108
X30
X511
X104
X1295
X1317
X1359
X1145
X1769
X2804
(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, 123 }: Central Line L(11, 123) { 100, 108 }: Central Line L(100, 108) { 30, 511 }: Central Line L(30, 511) { 104, 1295 }: Central Line L(104, 1295) { 1317, 1359 }: Central Line L(1317, 1359) { 1145, 1769 }: Central Line L(1145, 1769)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2720 = SR(X(100), X(108)) (0.8000, 0.4000) X_11 = FEUERBACH POINT (0.7200, 0.0400) X_123 = -OF-MEDIAL-TRIANGLE (0.5000, 0.0000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.6400, 0.4800) 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_1295 = COLLINGS TRANSFORM OF X(123) (0.3600, -0.4800) X_1317 = REFLECTION OF X(11) IN X(1) (0.4800, 0.3600) X_1359 = BRISSE TRANSFORM OF X(102) (0.6560, 0.3920) X_1145 = 3rd EHRMANN POINT (0.3200, 0.2400) X_1769 = MIMOSA TRANSFORM OF X(901) (1.2000, 0.4000) X_2804 = ISOGONAL CONJUGATE OF X(2720) (-0.0191, 0.0571)
A
B
C
X2720
X11
X123
X100
X108
X30
X511
X104
X1295
X1317
X1359
X1145
X1769
X2804
(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, 123 }: Central Line L(11, 123) { 100, 108 }: Central Line L(100, 108) { 30, 511 }: Central Line L(30, 511) { 104, 1295 }: Central Line L(104, 1295) { 1317, 1359 }: Central Line L(1317, 1359) { 1145, 1769 }: Central Line L(1145, 1769)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2720 = SR(X(100), X(108)) (0.7614, 0.4263) X_11 = FEUERBACH POINT (0.6897, 0.0298) X_123 = -OF-MEDIAL-TRIANGLE (0.5000, 0.0000) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.6180, 0.4859) 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_1295 = COLLINGS TRANSFORM OF X(123) (0.3820, -0.4859) X_1317 = REFLECTION OF X(11) IN X(1) (0.4784, 0.3744) X_1359 = BRISSE TRANSFORM OF X(102) (0.6318, 0.3985) X_1145 = 3rd EHRMANN POINT (0.3443, 0.2540) X_1769 = MIMOSA TRANSFORM OF X(901) (1.3003, 0.4042) X_2804 = ISOGONAL CONJUGATE OF X(2720) (-0.0287, 0.0727)
A
B
C
X2720
X11
X123
X100
X108
X30
X511
X104
X1295
X1317
X1359
X1145
X1769
X2804
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, 123 }: Central Line L(11, 123) { 100, 108 }: Central Line L(100, 108) { 30, 511 }: Central Line L(30, 511) { 104, 1295 }: Central Line L(104, 1295) { 1317, 1359 }: Central Line L(1317, 1359) { 1145, 1769 }: Central Line L(1145, 1769)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2720 = SR(X(100), X(108)) (0.6641, 0.2717) X_11 = FEUERBACH POINT (0.6563, 0.0066) X_123 = -OF-MEDIAL-TRIANGLE (0.4922, 0.0020) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_108 = Ψ(CIRCUMCENTER, INCENTER) (0.6487, 0.2761) 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_1295 = COLLINGS TRANSFORM OF X(123) (0.3513, -0.8254) X_1317 = REFLECTION OF X(11) IN X(1) (0.5745, 0.2534) X_1359 = BRISSE TRANSFORM OF X(102) (0.6493, 0.2556) X_1145 = 3rd EHRMANN POINT (0.3615, 0.1434) X_1769 = MIMOSA TRANSFORM OF X(901) (1.1349, 0.1652) X_2804 = ISOGONAL CONJUGATE OF X(2720) (-0.1114, 0.0749)
A
B
C
X2720
X11
X123
X100
X108
X30
X511
X104
X1295
X1317
X1359
X1145
X1769
X2804
Kimberling (6, 9, 13) | AB = 1
X2804 (ISOGONAL CONJUGATE OF X2720 ) 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
X2720 Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines6 lines
{11 123 30 511 100 108 104 1295 1145 1769 1317 1359
▸ Functional Relations2 relations
X2804 X2720
X2804 i -Ceva conjugate of Xj for these (i,j): (100 119 655 9 901 1329 1295 123 1320 11
Notes
Let Ia be the reflection of X1 BC , and define Ib and Ic cyclically. X2804 X521 Ia Ib Ic ; Ia Ib Ic is the inner Garcia triangle. (Randy Hutson , February 10, 2016)
