X799
ISOGONAL CONJUGATE OF X798
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) { 99, 100 }: Central Line L(99, 100) { 88, 274 }: Central Line L(88, 274) { 63, 561 }: Central Line L(63, 561) { 310, 333 }: Central Line L(310, 333) { 190, 670 }: Central Line L(190, 670) { 110, 789 }: Central Line L(110, 789)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-13.4299, 10.5763) X_99 = STEINER POINT (0.1109, 0.4322) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5168, 0.1843) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.4126, 0.1125) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4762, 0.1536) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4886, 0.1475) X_190 = YFF PARABOLIC POINT (0.0748, 0.3999) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (-0.0057, 0.2948) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.0826, 0.3957) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636)
A
B
C
X798
X99
X100
X88
X274
X63
X561
X310
X333
X190
X670
X110
X789
X799
(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) { 99, 100 }: Central Line L(99, 100) { 88, 274 }: Central Line L(88, 274) { 63, 561 }: Central Line L(63, 561) { 310, 333 }: Central Line L(310, 333) { 190, 670 }: Central Line L(190, 670) { 110, 789 }: Central Line L(110, 789)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-4.9362, 4.4681) X_99 = STEINER POINT (0.1511, 0.3581) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2000, 0.4000) X_88 = ISOGONAL CONJUGATE OF X(44) (1.0000, 0.0000) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5114, 0.1416) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4286, 0.0000) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.3420, 0.0633) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4433, 0.1060) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4702, 0.0944) X_190 = YFF PARABOLIC POINT (0.0933, 0.3200) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (-0.0176, 0.1938) X_110 = FOCUS OF KIEPERT PARABOLA (0.3600, 0.4800) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.1092, 0.3119) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0532, 0.2744)
A
B
C
X798
X99
X100
X88
X274
X63
X561
X310
X333
X190
X670
X110
X789
X799
(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) { 99, 100 }: Central Line L(99, 100) { 88, 274 }: Central Line L(88, 274) { 63, 561 }: Central Line L(63, 561) { 310, 333 }: Central Line L(310, 333) { 190, 670 }: Central Line L(190, 670) { 110, 789 }: Central Line L(110, 789)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-5.9482, 4.4191) X_99 = STEINER POINT (0.1910, 0.3931) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.2386, 0.4263) X_88 = ISOGONAL CONJUGATE OF X(44) (0.9710, -0.0490) X_274 = ISOGONAL CONJUGATE OF X(213) (0.5101, 0.1439) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4401, 0.0000) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.3669, 0.0666) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.4532, 0.1089) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4753, 0.0961) X_190 = YFF PARABOLIC POINT (0.1322, 0.3610) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (0.0000, 0.2429) X_110 = FOCUS OF KIEPERT PARABOLA (0.3820, 0.4859) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.1475, 0.3546) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0873, 0.3209)
A
B
C
X798
X99
X100
X88
X274
X63
X561
X310
X333
X190
X670
X110
X789
X799
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) { 99, 100 }: Central Line L(99, 100) { 88, 274 }: Central Line L(88, 274) { 63, 561 }: Central Line L(63, 561) { 310, 333 }: Central Line L(310, 333) { 190, 670 }: Central Line L(190, 670) { 110, 789 }: Central Line L(110, 789)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_798 = CROSSDIFFERENCE OF X(1) AND X(75) (-1.6429, 1.3237) X_99 = STEINER POINT (0.2513, 0.2387) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.3206, 0.2669) X_88 = ISOGONAL CONJUGATE OF X(44) (0.9802, -0.0393) X_274 = ISOGONAL CONJUGATE OF X(213) (0.4902, 0.0774) X_63 = ISOGONAL CONJUGATE OF X(19) (0.3991, -0.1098) X_561 = ISOGONAL CONJUGATE OF 4th POWER POINT (0.2571, 0.0197) X_310 = ISOTOMIC CONJUGATE OF X(42) (0.3899, 0.0479) X_333 = CEVAPOINT OF X(8) AND X(9) (0.4404, 0.0269) X_190 = YFF PARABOLIC POINT (0.1548, 0.2119) X_670 = TRILINEAR POLE OF LINE X(2)X(39) (-0.0270, 0.1039) X_110 = FOCUS OF KIEPERT PARABOLA (0.4975, 0.2958) X_789 = o-(- 3, 0) CIRCUMCIRCLE POINT (0.1873, 0.2025) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0892, 0.1730)
A
B
C
X798
X99
X100
X88
X274
X63
X561
X310
X333
X190
X670
X110
X789
X799
Kimberling (6, 9, 13) | AB = 1
X799 (ISOGONAL CONJUGATE OF X798 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(\csc^{2} A/(\cos^{2} B - \cos^{2} C) : :\)
Barycentrics: \((\csc A)/(\cos^{2} B - \cos^{2} C) : :\)
Search Value (6, 9, 13): \(5.397410202348\)
▸ Alternate Coordinates1 form
▸ Incident Central Lines11 lines
{2 873 63 561 75 897 88 274 99 100 110 789 162 811 190 670 310 333 645 651 689 813
▸ Functional Relations10 relations
Notes
Let La be the A-extraversion of line X1 X75 Lb and Lc cyclically. Let A' = Lb ∩ Lc , and define B' and C' cyclically. The lines AA' , BB' , CC' concur in X799 Randy Hutson , January 29, 2018)
As the trilinear product of Steiner circumellipse antipodes, X799 A , B , C ,X668 X789 6376 and perspector X75
