X1501
TRILINEAR 5th POWER POINT
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) { 6, 22 }: Central Line L(6, 22) { 32, 184 }: Central Line L(32, 184) { 101, 697 }: Central Line L(101, 697) { 110, 699 }: Central Line L(110, 699) { 154, 1184 }: Central Line L(154, 1184) { 701, 825 }: Central Line L(701, 825)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.3682, 0.0896) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_22 = EXETER POINT (0.4143, -0.1221) X_32 = 3rd POWER POINT (0.6400, 0.3332) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.5788, 0.1496) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_697 = EVEN (- 4, - 3) CIRCUMCIRCLE POINT (0.9705, 0.2996) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9822, 0.2692) X_154 = -CEVA CONJUGATE OF X(6) (0.4807, -0.3954) X_1184 = 2nd SARAGOSSA POINT OF X(25) (0.6413, 0.3116) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.9924, 0.2359) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.2886, 0.5665) X_1501 = TRILINEAR 5th POWER POINT (0.6596, 0.3922)
A
B
C
X1502
X6
X22
X32
X184
X101
X697
X110
X699
X154
X1184
X701
X825
X1501
(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) { 6, 22 }: Central Line L(6, 22) { 32, 184 }: Central Line L(32, 184) { 101, 697 }: Central Line L(101, 697) { 110, 699 }: Central Line L(110, 699) { 154, 1184 }: Central Line L(154, 1184) { 701, 825 }: Central Line L(701, 825)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.2762, 0.0430) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_22 = EXETER POINT (0.3600, -0.4800) X_32 = 3rd POWER POINT (0.6819, 0.3119) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6400, 0.0000) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3077, 0.4615) X_697 = EVEN (- 4, - 3) CIRCUMCIRCLE POINT (0.8859, 0.3179) X_110 = FOCUS OF KIEPERT PARABOLA (0.3600, 0.4800) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9056, 0.2923) X_154 = -CEVA CONJUGATE OF X(6) (0.5467, 0.7350) X_1184 = 2nd SARAGOSSA POINT OF X(25) (0.6893, 0.2822) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.9259, 0.2619) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.4079, 0.4914) X_1501 = TRILINEAR 5th POWER POINT (0.6893, 0.3667)
A
B
C
X1502
X6
X22
X32
X184
X101
X697
X110
X699
X154
X1184
X701
X825
X1501
(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) { 6, 22 }: Central Line L(6, 22) { 32, 184 }: Central Line L(32, 184) { 101, 697 }: Central Line L(101, 697) { 110, 699 }: Central Line L(110, 699) { 154, 1184 }: Central Line L(154, 1184) { 701, 825 }: Central Line L(701, 825)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.3090, 0.0464) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_22 = EXETER POINT (0.3820, -0.4859) X_32 = 3rd POWER POINT (0.6545, 0.3180) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.6180, 0.0000) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.3365, 0.4725) X_697 = EVEN (- 4, - 3) CIRCUMCIRCLE POINT (0.8949, 0.3067) X_110 = FOCUS OF KIEPERT PARABOLA (0.3820, 0.4859) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9173, 0.2754) X_154 = -CEVA CONJUGATE OF X(6) (0.5393, 0.7370) X_1184 = 2nd SARAGOSSA POINT OF X(25) (0.6612, 0.2873) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.9395, 0.2384) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.4229, 0.4940) X_1501 = TRILINEAR 5th POWER POINT (0.6612, 0.3761)
A
B
C
X1502
X6
X22
X32
X184
X101
X697
X110
X699
X154
X1184
X701
X825
X1501
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) { 6, 22 }: Central Line L(6, 22) { 32, 184 }: Central Line L(32, 184) { 101, 697 }: Central Line L(101, 697) { 110, 699 }: Central Line L(110, 699) { 154, 1184 }: Central Line L(154, 1184) { 701, 825 }: Central Line L(701, 825)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1502 = ISOGONAL CONJUGATE OF X(1501) (0.1820, 0.0102) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_22 = EXETER POINT (0.8328, 2.4854) X_32 = 3rd POWER POINT (0.6767, 0.2196) X_184 = INVERSE OF X(125) IN THE BROCARD CIRCLE (0.3215, 1.0549) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.4482, 0.2934) X_697 = EVEN (- 4, - 3) CIRCUMCIRCLE POINT (0.7674, 0.2293) X_110 = FOCUS OF KIEPERT PARABOLA (0.4975, 0.2958) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.7937, 0.2144) X_154 = -CEVA CONJUGATE OF X(6) (0.5294, 0.5043) X_1184 = 2nd SARAGOSSA POINT OF X(25) (0.6956, 0.1899) X_701 = EVEN (- 4, - 1) CIRCUMCIRCLE POINT (0.8256, 0.1938) X_825 = o-(0, 3) CIRCUMCIRCLE POINT (0.5356, 0.2947) X_1501 = TRILINEAR 5th POWER POINT (0.6637, 0.2501)
A
B
C
X1502
X6
X22
X32
X184
X101
X697
X110
X699
X154
X1184
X701
X825
X1501
Kimberling (6, 9, 13) | AB = 1
X1501 (TRILINEAR 5th POWER POINT ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a^{5}: b^{5} : c^{5}\)
Barycentrics: \(a^{6} : b^{6} : c^{6}\)
Search Value (6, 9, 13): \(0.068091376825\)
▸ Incident Central Lines8 lines
{6 22 32 184 101 697 110 699 154 1184 701 825 703 827 1196 1495
▸ Functional Relations11 relations
Notes
X1501 vertex conjugate of the foci of the inellipse that is the barycentric square of the Lemoine axis. The center of this inellipse is X8265 and its perspector is X32 Randy Hutson , October 15, 2018)
