X2493
RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE}
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) { 5, 39 }: Central Line L(5, 39) { 23, 50 }: Central Line L(23, 50) { 2, 94 }: Central Line L(2, 94) { 6, 110 }: Central Line L(6, 110) { 24, 112 }: Central Line L(24, 112) { 53, 136 }: Central Line L(53, 136)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_842 = ISOGONAL CONJUGATE OF X(542) (-0.0101, 0.1156) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_50 = -CEVA CONJUGATE OF X(184) (2.1559, 2.8368) X_94 = ISOGONAL CONJUGATE OF X(50) (0.9069, -0.1331) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.6627, 0.5278) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.5162, 0.6121) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6164, 0.4390) X_136 = INTERSECTION OF LINE X(4)X(110) AND X(25)X(132) (0.8024, 0.3155) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (-0.6894, 1.3058)
A
B
C
X2
X842
X5
X39
X23
X50
X94
X6
X110
X24
X112
X53
X136
X2493
(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) { 5, 39 }: Central Line L(5, 39) { 23, 50 }: Central Line L(23, 50) { 2, 94 }: Central Line L(2, 94) { 6, 110 }: Central Line L(6, 110) { 230, 231 }: Central Line L(230, 231) { 25, 1576 }: Central Line L(25, 1576)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_2 = CENTROID (0.5467, 0.1600) X_842 = ISOGONAL CONJUGATE OF X(542) (0.0133, -0.1144) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_39 = BROCARD MIDPOINT (0.6138, 0.1951) X_23 = FAR-OUT POINT (0.9200, 1.4400) X_50 = -CEVA CONJUGATE OF X(184) (2.2857, 3.0612) X_94 = ISOGONAL CONJUGATE OF X(50) (0.8532, -0.2508) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_110 = FOCUS OF KIEPERT PARABOLA (0.3600, 0.4800) X_230 = -CEVA CONJUGATE OF X(114) (0.8489, 0.4191) X_231 = -CEVA CONJUGATE OF X(128) (0.9181, 0.3989) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6400, 0.4800) X_1576 = ISOGONAL CONJUGATE OF X(850) (0.5000, 0.5208) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (0.2156, 0.6038)
A
B
C
X2
X842
X5
X39
X23
X50
X94
X6
X110
X230
X231
X25
X1576
X2493
(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) { 5, 39 }: Central Line L(5, 39) { 23, 50 }: Central Line L(23, 50) { 2, 94 }: Central Line L(2, 94) { 6, 110 }: Central Line L(6, 110) { 230, 231 }: Central Line L(230, 231) { 25, 1576 }: Central Line L(25, 1576)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_2 = CENTROID (0.5393, 0.1620) X_842 = ISOGONAL CONJUGATE OF X(542) (0.0451, -0.2075) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_39 = BROCARD MIDPOINT (0.5955, 0.1965) X_23 = FAR-OUT POINT (0.8541, 1.4576) X_50 = -CEVA CONJUGATE OF X(184) (2.6180, 4.3593) X_94 = ISOGONAL CONJUGATE OF X(50) (0.8111, -0.3087) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_110 = FOCUS OF KIEPERT PARABOLA (0.3820, 0.4859) X_230 = -CEVA CONJUGATE OF X(114) (0.8090, 0.4395) X_231 = -CEVA CONJUGATE OF X(128) (0.8795, 0.4223) X_25 = HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES (0.6180, 0.4859) X_1576 = ISOGONAL CONJUGATE OF X(850) (0.5000, 0.5145) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (0.3090, 0.5609)
A
B
C
X2
X842
X5
X39
X23
X50
X94
X6
X110
X230
X231
X25
X1576
X2493
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) { 5, 39 }: Central Line L(5, 39) { 23, 50 }: Central Line L(23, 50) { 2, 94 }: Central Line L(2, 94) { 6, 110 }: Central Line L(6, 110) { 24, 112 }: Central Line L(24, 112) { 53, 136 }: Central Line L(53, 136)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_2 = CENTROID (0.5444, 0.0934) X_842 = ISOGONAL CONJUGATE OF X(542) (0.1364, -0.7143) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_39 = BROCARD MIDPOINT (0.6418, 0.1220) X_23 = FAR-OUT POINT (0.6051, 0.5970) X_50 = -CEVA CONJUGATE OF X(184) (0.5919, -0.0176) X_94 = ISOGONAL CONJUGATE OF X(50) (0.6355, 0.3039) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_110 = FOCUS OF KIEPERT PARABOLA (0.4975, 0.2958) X_24 = PERSPECTOR OF ABC AND ORTHIC-OF-ORTHIC TRIANGLE (0.5555, 0.1854) X_112 = Ψ(ORTHOCENTER, SYMMEDIAN POINT) (0.6732, 0.2689) X_53 = SYMMEDIAN POINT OF ORTHIC TRIANGLE (0.6533, 0.2777) X_136 = INTERSECTION OF LINE X(4)X(110) AND X(25)X(132) (0.4292, 0.0274) X_2493 = RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} (0.5969, 0.2147)
A
B
C
X2
X842
X5
X39
X23
X50
X94
X6
X110
X24
X112
X53
X136
X2493
Kimberling (6, 9, 13) | AB = 1
X2493 (RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, PARRY CIRCLE} ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a[a^{6}(b^{2} + c^{2}) - a^{4}(b^{2} + c^{2})^{2} - a^{2}(b^{6} + c^{6} - 2b^{4}c^{2} - 2b^{2}c^{4}) + (b^{4} + c^{4} - b^{2}c^{2})(b^{2} - c^{2})^{2}] : :\)
Search Value (6, 9, 13): \(0.960644034227\)
▸ Incident Central Lines10 lines
{2 94 5 39 6 110 23 50 24 112 25 1576 53 136 216 3054 230 231 1084 1196
▸ Functional Relations3 relations
