X2503
RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN 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) { 6, 110 }: Central Line L(6, 110) { 44, 513 }: Central Line L(44, 513) { 37, 2611 }: Central Line L(37, 2611)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_842 = ISOGONAL CONJUGATE OF X(542) (-0.0101, 0.1156) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_110 = FOCUS OF KIEPERT PARABOLA (0.2516, 0.5478) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_2611 = DIFFERENCE OF PU(71) (0.7448, 0.0628) X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} (-9.6316, 8.5088)
A
B
C
X842
X55
X6
X110
X44
X513
X37
X2611
X2503
(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, 110 }: Central Line L(6, 110) { 44, 513 }: Central Line L(44, 513) { 37, 2611 }: Central Line L(37, 2611)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_842 = ISOGONAL CONJUGATE OF X(542) (0.0133, -0.1144) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5714, 0.1429) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_110 = FOCUS OF KIEPERT PARABOLA (0.3600, 0.4800) X_44 = -LINE CONJUGATE OF X(1) (1.6000, 1.2000) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0610, -0.0971) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_2611 = DIFFERENCE OF PU(71) (0.7429, 0.0333) X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} (-3.3920, 3.6960)
A
B
C
X842
X55
X6
X110
X44
X513
X37
X2611
X2503
(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, 110 }: Central Line L(6, 110) { 44, 513 }: Central Line L(44, 513) { 37, 2611 }: Central Line L(37, 2611)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_842 = ISOGONAL CONJUGATE OF X(542) (0.0451, -0.2075) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5599, 0.1439) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_110 = FOCUS OF KIEPERT PARABOLA (0.3820, 0.4859) X_44 = -LINE CONJUGATE OF X(1) (1.5111, 1.3165) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0703, -0.0589) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_2611 = DIFFERENCE OF PU(71) (0.7103, 0.0248) X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} (-1.7387, 2.6682)
A
B
C
X842
X55
X6
X110
X44
X513
X37
X2611
X2503
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, 110 }: Central Line L(6, 110) { 44, 513 }: Central Line L(44, 513) { 37, 2611 }: Central Line L(37, 2611)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_842 = ISOGONAL CONJUGATE OF X(542) (0.1364, -0.7143) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5940, 0.0549) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_110 = FOCUS OF KIEPERT PARABOLA (0.4975, 0.2958) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_2611 = DIFFERENCE OF PU(71) (0.7076, 0.0004) X_2503 = RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} (-0.2908, 0.9383)
A
B
C
X842
X55
X6
X110
X44
X513
X37
X2611
X2503
Kimberling (6, 9, 13) | AB = 1
X2503 (RADICAL CENTER OF {CIRCUMCIRCLE, PARRY CIRCLE, BEVAN CIRCLE} ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) , where \(f(a,b,c) = a(b + c)[a^{4} - b^{4} - c^{4} + bc(b^{2} + bc + c^{2} - 2a^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(0.486805033581\)
▸ Incident Central Lines3 lines
{6 110 37 2611 44 513
▸ Functional Relations1 relation
