X2525
RADICAL CENTER OF {NINE-POINT, BROCARD, (X4 ,2R)} CIRCLES
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) { 441, 525 }: Central Line L(441, 525) { 669, 690 }: Central Line L(669, 690) { 826, 2474 }: Central Line L(826, 2474) { 523, 2526 }: Central Line L(523, 2526)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.3258, 0.0397) X_125 = CENTER OF JERABEK HYPERBOLA (0.6803, 0.0260) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0840, -0.1726) X_826 = ODD (0, 4) INFINITY POINT (1.1003, 0.0340) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (6.9649, -4.0371) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0856, -0.0096) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (37.2857, -17.0298) X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-9.1140, 0.7037)
A
B
C
X305
X125
X441
X525
X669
X690
X826
X2474
X523
X2526
X2525
(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) { 441, 525 }: Central Line L(441, 525) { 669, 690 }: Central Line L(669, 690) { 826, 2474 }: Central Line L(826, 2474) { 523, 2526 }: Central Line L(523, 2526)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.2404, 0.0000) X_125 = CENTER OF JERABEK HYPERBOLA (0.6400, 0.0000) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-1.2857, 2.0833) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0500, -0.1297) X_826 = ODD (0, 4) INFINITY POINT (1.1111, 0.0502) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (3.3886, -1.6033) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0987, -0.0010) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (16.4000, -6.2000) X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-4.8571, 0.0000)
A
B
C
X305
X125
X441
X525
X669
X690
X826
X2474
X523
X2526
X2525
(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) { 441, 525 }: Central Line L(441, 525) { 669, 690 }: Central Line L(669, 690) { 826, 2474 }: Central Line L(826, 2474) { 523, 2526 }: Central Line L(523, 2526)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.2764, 0.0000) X_125 = CENTER OF JERABEK HYPERBOLA (0.6180, 0.0000) X_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-1.6180, 2.0582) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (0.0222, -0.0893) X_826 = ODD (0, 4) INFINITY POINT (1.1069, 0.0700) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (3.8541, -1.5723) X_523 = ISOGONAL CONJUGATE OF X(110) (1.0981, 0.0262) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (19.4627, -6.1503) X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-5.8541, 0.0000)
A
B
C
X305
X125
X441
X525
X669
X690
X826
X2474
X523
X2526
X2525
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) { 441, 525 }: Central Line L(441, 525) { 669, 690 }: Central Line L(669, 690) { 826, 2474 }: Central Line L(826, 2474) { 523, 2526 }: Central Line L(523, 2526)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_305 = ISOTOMIC CONJUGATE OF X(25) (0.1864, -0.0120) X_125 = CENTER OF JERABEK HYPERBOLA (0.5678, -0.0079) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-0.1118, 0.6834) X_690 = CROSSDIFFERENCE OF LINE X(6) AND X(110) (-0.0947, -0.0548) X_826 = ODD (0, 4) INFINITY POINT (1.1992, 0.0530) X_2474 = RADICAL CENTER OF {BROCARD, 2nd LEMOINE, (X(4),2R)} CIRCLES (2.0285, -0.4057) X_523 = ISOGONAL CONJUGATE OF X(110) (1.1957, 0.0148) X_2526 = RADICAL CENTER OF {NINE-POINT, APOLLONIUS, (X(4),2R)} CIRCLES (8.1142, -1.4581) X_2525 = RADICAL CENTER OF {NINE-POINT, BROCARD, (X(4),2R)} CIRCLES (-3.3742, -0.0728)
A
B
C
X305
X125
X441
X525
X669
X690
X826
X2474
X523
X2526
X2525
Kimberling (6, 9, 13) | AB = 1
X2525 (RADICAL CENTER OF {NINE-POINT, BROCARD, (X4 ,2R)} CIRCLES ) 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 \(f(a,b,c) = bc(b^{4} - c^{4})(b^{2} + c^{2} - a^{2})\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(35.255947468207\)
▸ Incident Central Lines4 lines
▸ Functional Relations4 relations
