X2783
ISOGONAL CONJUGATE OF X2699
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, 114 }: Central Line L(11, 114) { 98, 100 }: Central Line L(98, 100) { 99, 104 }: Central Line L(99, 104) { 115, 119 }: Central Line L(115, 119) { 147, 149 }: Central Line L(147, 149) { 148, 153 }: Central Line L(148, 153)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2699 = SR(X(98), X(100)) (0.0115, 0.2496) X_11 = FEUERBACH POINT (0.7347, 0.0667) X_114 = KIEPERT ANTIPODE (0.3616, 0.4140) X_98 = TARRY POINT (0.8891, -0.2281) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_99 = STEINER POINT (0.1109, 0.4322) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_153 = REFLECTION OF X(20) IN X(100) (-0.1020, 1.1248) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.1079, 0.5998)
A
B
C
X2699
X11
X114
X98
X100
X99
X104
X115
X119
X147
X149
X148
X153
X2783
(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, 114 }: Central Line L(11, 114) { 98, 100 }: Central Line L(98, 100) { 99, 104 }: Central Line L(99, 104) { 115, 119 }: Central Line L(115, 119) { 147, 149 }: Central Line L(147, 149) { 148, 153 }: Central Line L(148, 153)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2699 = SR(X(98), X(100)) (0.0041, 0.0642) X_11 = FEUERBACH POINT (0.7200, 0.0400) X_114 = KIEPERT ANTIPODE (0.3955, 0.4191) X_98 = TARRY POINT (0.8489, -0.3581) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_99 = STEINER POINT (0.1511, 0.3581) X_104 = ANTIPODE OF X(100) (0.8000, -0.4000) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7445, 0.0609) X_119 = FEUERBACH ANTIPODE (0.4200, 0.4400) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.0578, 1.1963) X_149 = REFLECTION OF X(20) IN X(104) (1.2400, -0.3200) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3378, -0.2363) X_153 = REFLECTION OF X(20) IN X(100) (0.0400, 1.2800) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.1728, 0.5968)
A
B
C
X2699
X11
X114
X98
X100
X99
X104
X115
X119
X147
X149
X148
X153
X2783
(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, 114 }: Central Line L(11, 114) { 98, 100 }: Central Line L(98, 100) { 99, 104 }: Central Line L(99, 104) { 115, 119 }: Central Line L(115, 119) { 147, 149 }: Central Line L(147, 149) { 148, 153 }: Central Line L(148, 153)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2699 = SR(X(98), X(100)) (0.0034, -0.0580) X_11 = FEUERBACH POINT (0.6897, 0.0298) X_114 = KIEPERT ANTIPODE (0.4045, 0.4395) X_98 = TARRY POINT (0.8090, -0.3931) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_99 = STEINER POINT (0.1910, 0.3931) X_104 = ANTIPODE OF X(100) (0.7614, -0.4263) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7135, 0.0464) X_119 = FEUERBACH ANTIPODE (0.4283, 0.4561) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.0000, 1.2720) X_149 = REFLECTION OF X(20) IN X(104) (1.1407, -0.3666) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.2361, -0.3003) X_153 = REFLECTION OF X(20) IN X(100) (0.0953, 1.3384) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.2108, 0.6339)
A
B
C
X2699
X11
X114
X98
X100
X99
X104
X115
X119
X147
X149
X148
X153
X2783
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, 114 }: Central Line L(11, 114) { 98, 100 }: Central Line L(98, 100) { 99, 104 }: Central Line L(99, 104) { 115, 119 }: Central Line L(115, 119) { 147, 149 }: Central Line L(147, 149) { 148, 153 }: Central Line L(148, 153)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2699 = SR(X(98), X(100)) (0.0179, -0.5798) X_11 = FEUERBACH POINT (0.6563, 0.0066) X_114 = KIEPERT ANTIPODE (0.4422, 0.5341) X_98 = TARRY POINT (0.7487, -0.7881) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_99 = STEINER POINT (0.2513, 0.2387) X_104 = ANTIPODE OF X(100) (0.6794, -0.8162) X_115 = CENTER OF KIEPERT HYPERBOLA (0.6909, 0.0207) X_119 = FEUERBACH ANTIPODE (0.4769, 0.5481) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.1358, 1.8562) X_149 = REFLECTION OF X(20) IN X(104) (0.9920, -0.2537) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.1305, -0.1974) X_153 = REFLECTION OF X(20) IN X(100) (0.2743, 1.9125) X_2783 = ISOGONAL CONJUGATE OF X(2699) (0.2977, 0.7013)
A
B
C
X2699
X11
X114
X98
X100
X99
X104
X115
X119
X147
X149
X148
X153
X2783
Kimberling (6, 9, 13) | AB = 1
X2783 (ISOGONAL CONJUGATE OF X2699 ) 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
X2699 Barycentrics: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\)
▸ Incident Central Lines11 lines
{5 2486 11 114 30 511 80 256 98 100 99 104 115 119 147 149 148 153 1284 1733 1764 1768
▸ Functional Relations4 relations
Notes
Let Ia be the reflection of X1 BC , and define Ib and Ic cyclically; then X2783 X511 Ia Ib Ic ; “Ia Ib Ic is the inner Garcia triangle. (Randy Hutson , February 10, 2016)
