X2896
ANTICOMPLEMENTARY CONJUGATE OF X76
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) { 2, 32 }: Central Line L(2, 32) { 3, 147 }: Central Line L(3, 147) { 76, 148 }: Central Line L(76, 148) { 69, 194 }: Central Line L(69, 194) { 141, 384 }: Central Line L(141, 384) { 15, 628 }: Central Line L(15, 628)
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_32 = 3rd POWER POINT (0.6400, 0.3332) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.1660, 1.0561) X_76 = 3rd BROCARD POINT (0.4567, 0.1388) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3904, -0.2646) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5061, 0.1663) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_15 = 1st ISODYNAMIC POINT (0.5519, 0.1878) X_628 = ANTICOMPLEMENT OF X(18) (0.7255, 0.3365) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4820, 0.1279)
A
B
C
X2
X32
X3
X147
X76
X148
X69
X194
X141
X384
X15
X628
X2896
(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) { 2, 32 }: Central Line L(2, 32) { 3, 147 }: Central Line L(3, 147) { 76, 148 }: Central Line L(76, 148) { 69, 194 }: Central Line L(69, 194) { 141, 384 }: Central Line L(141, 384) { 15, 628 }: Central Line L(15, 628)
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_32 = 3rd POWER POINT (0.6819, 0.3119) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (-0.0578, 1.1963) X_76 = 3rd BROCARD POINT (0.4124, 0.0899) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.3378, -0.2363) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3600, 0.0000) X_194 = -CEVA CONJUGATE OF X(2) (0.8151, 0.3002) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5000, 0.1200) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5622, 0.2132) X_15 = 1st ISODYNAMIC POINT (0.5764, 0.1310) X_628 = ANTICOMPLEMENT OF X(18) (0.9636, 0.3449) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4671, 0.0706)
A
B
C
X2
X32
X3
X147
X76
X148
X69
X194
X141
X384
X15
X628
X2896
(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) { 2, 32 }: Central Line L(2, 32) { 3, 147 }: Central Line L(3, 147) { 76, 148 }: Central Line L(76, 148) { 69, 194 }: Central Line L(69, 194) { 141, 384 }: Central Line L(141, 384) { 15, 628 }: Central Line L(15, 628)
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_32 = 3rd POWER POINT (0.6545, 0.3180) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.0000, 1.2720) X_76 = 3rd BROCARD POINT (0.4271, 0.0928) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.2361, -0.3003) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3820, 0.0000) X_194 = -CEVA CONJUGATE OF X(2) (0.7639, 0.3003) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.5000, 0.1215) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5528, 0.2173) X_15 = 1st ISODYNAMIC POINT (0.5641, 0.1319) X_628 = ANTICOMPLEMENT OF X(18) (0.8754, 0.3386) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4721, 0.0709)
A
B
C
X2
X32
X3
X147
X76
X148
X69
X194
X141
X384
X15
X628
X2896
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) { 2, 32 }: Central Line L(2, 32) { 3, 147 }: Central Line L(3, 147) { 76, 148 }: Central Line L(76, 148) { 69, 194 }: Central Line L(69, 194) { 141, 384 }: Central Line L(141, 384) { 15, 628 }: Central Line L(15, 628)
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_32 = 3rd POWER POINT (0.6767, 0.2196) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE (0.1358, 1.8562) X_76 = 3rd BROCARD POINT (0.3495, 0.0360) X_148 = STEINER POINT OF ANTICOMPLEMENTARY TRIANGLE (1.1305, -0.1974) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3185, -0.0509) X_194 = -CEVA CONJUGATE OF X(2) (0.9341, 0.2081) X_141 = COMPLEMENT OF SYMMEDIAN POINT (0.4879, 0.0573) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5511, 0.1491) X_15 = 1st ISODYNAMIC POINT (0.6000, 0.0051) X_628 = ANTICOMPLEMENT OF X(18) (-4.1438, 0.0121) X_2896 = ANTICOMPLEMENTARY CONJUGATE OF X(76) (0.4521, 0.0053)
A
B
C
X2
X32
X3
X147
X76
X148
X69
X194
X141
X384
X15
X628
X2896
Kimberling (6, 9, 13) | AB = 1
X2896 (ANTICOMPLEMENTARY CONJUGATE OF X76 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(bc(b^{4} + c^{4} - a^{4} + b^{2}c^{2} + c^{2}a^{2} + a^{2}b^{2}) : :\) (M. Iliev, 5/13/07)
Search Value (6, 9, 13): \(4.266606038403\)
▸ Incident Central Lines9 lines
{2 32 3 147 15 628 16 627 20 1352 69 194 76 148 141 384 599 1975
▸ Functional Relations14 relations
Notes
Let A'B'C' be the 1st Brocard triangle and A″B″C″ the 1st Brocard-reflected triangle. Let A* be the isogonal conjugate of A″ , and define B* and C* cyclically. The lines A'A* , B'B* , C'C* concur in X2896 Randy Hutson , June 7, 2019)
Let OA be the circle centered at the A -vertex of the 2nd Neuberg triangle and passing through A ; define OB and OC cyclically. X2896 OA , OB , OC . (Randy Hutson, August 28, 2020)
