X2522
RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} 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) { 44, 513 }: Central Line L(44, 513) { 441, 525 }: Central Line L(441, 525) { 1021, 1734 }: Central Line L(1021, 1734)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_44 = -LINE CONJUGATE OF X(1) (2.1429, 2.0996) X_513 = ISOGONAL CONJUGATE OF X(100) (1.0529, -0.0806) X_441 = COMPLEMENT OF X(297) (0.3841, -0.2011) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0468, 0.2556) X_1021 = ISOGONAL CONJUGATE OF X(1020) (24.7475, -5.0780) X_1734 = MIMOSA TRANSFORM OF X(101) (10.6667, -1.6330) X_2522 = RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} CIRCLES (7.6393, -0.8923)
A
B
C
X44
X513
X441
X525
X1021
X1734
X2522
(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) { 44, 513 }: Central Line L(44, 513) { 441, 525 }: Central Line L(441, 525) { 1021, 1734 }: Central Line L(1021, 1734)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 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_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0283, 0.1600) X_1021 = ISOGONAL CONJUGATE OF X(1020) (12.4000, -1.2000) X_1734 = MIMOSA TRANSFORM OF X(101) (5.4000, -0.2000) X_2522 = RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} CIRCLES (4.0000, 0.0000)
A
B
C
X44
X513
X441
X525
X1021
X1734
X2522
(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) { 44, 513 }: Central Line L(44, 513) { 441, 525 }: Central Line L(441, 525) { 1021, 1734 }: Central Line L(1021, 1734)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 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_441 = COMPLEMENT OF X(297) (0.5000, 0.0000) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.0357, 0.1620) X_1021 = ISOGONAL CONJUGATE OF X(1020) (14.7166, -1.2021) X_1734 = MIMOSA TRANSFORM OF X(101) (6.3642, -0.2021) X_2522 = RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} CIRCLES (4.6762, 0.0000)
A
B
C
X44
X513
X441
X525
X1021
X1734
X2522
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) { 44, 513 }: Central Line L(44, 513) { 441, 525 }: Central Line L(441, 525) { 1021, 1734 }: Central Line L(1021, 1734)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_44 = -LINE CONJUGATE OF X(1) (1.1019, 0.5412) X_513 = ISOGONAL CONJUGATE OF X(100) (1.1753, -0.0865) X_441 = COMPLEMENT OF X(297) (0.5416, 0.0700) X_525 = ISOGONAL CONJUGATE OF X(112) (-0.1112, 0.0694) X_1021 = ISOGONAL CONJUGATE OF X(1020) (7.7553, -0.0695) X_1734 = MIMOSA TRANSFORM OF X(101) (3.2520, 0.1114) X_2522 = RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} CIRCLES (2.5036, 0.1415)
A
B
C
X44
X513
X441
X525
X1021
X1734
X2522
Kimberling (6, 9, 13) | AB = 1
X2522 (RADICAL CENTER OF {NINE-POINT,BROCARD, APOLLONIUS} CIRCLES ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \((b - c)(b^{2} + c^{2} - a^{2})(a^{2} + (b + c)^{2})\)
Search Value (6, 9, 13): \(-13.323242026659\)
▸ Incident Central Lines3 lines
▸ Functional Relations2 relations
