X695
ISOGONAL CONJUGATE OF X384
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) { 69, 194 }: Central Line L(69, 194) { 248, 682 }: Central Line L(248, 682) { 384, 694 }: Central Line L(384, 694) { 99, 711 }: Central Line L(99, 711)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5532, 0.2412) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.4122, 0.0654) X_194 = -CEVA CONJUGATE OF X(2) (0.6989, 0.3222) X_248 = -LINE CONJUGATE OF X(132) (0.8229, -0.0790) X_682 = POINT ARNEB (0.6397, 0.1604) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0179, 0.0378) X_99 = STEINER POINT (0.1109, 0.4322) X_711 = EVEN (- 4, 4) CIRCUMCIRCLE POINT (1.0071, 0.0447) X_695 = ISOGONAL CONJUGATE OF X(384) (0.5903, 0.2249)
A
B
C
X384
X69
X194
X248
X682
X694
X99
X711
X695
(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) { 69, 194 }: Central Line L(69, 194) { 384, 694 }: Central Line L(384, 694) { 99, 711 }: Central Line L(99, 711)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5622, 0.2132) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3600, 0.0000) X_194 = -CEVA CONJUGATE OF X(2) (0.8151, 0.3002) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0176, 0.0462) X_99 = STEINER POINT (0.1511, 0.3581) X_711 = EVEN (- 4, 4) CIRCUMCIRCLE POINT (0.9966, 0.0582) X_695 = ISOGONAL CONJUGATE OF X(384) (0.6400, 0.1847)
A
B
C
X384
X69
X194
X694
X99
X711
X695
(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) { 69, 194 }: Central Line L(69, 194) { 384, 694 }: Central Line L(384, 694) { 99, 711 }: Central Line L(99, 711)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5528, 0.2173) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3820, 0.0000) X_194 = -CEVA CONJUGATE OF X(2) (0.7639, 0.3003) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0000, 0.0000) X_99 = STEINER POINT (0.1910, 0.3931) X_711 = EVEN (- 4, 4) CIRCUMCIRCLE POINT (1.0000, 0.0000) X_695 = ISOGONAL CONJUGATE OF X(384) (0.6180, 0.1856)
A
B
C
X384
X69
X194
X694
X99
X711
X695
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) { 69, 194 }: Central Line L(69, 194) { 248, 682 }: Central Line L(248, 682) { 384, 694 }: Central Line L(384, 694) { 99, 711 }: Central Line L(99, 711)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_384 = THE CONWAY POINT: EULER LINE INTERCEPT OF LINE X(32)X(76) (0.5511, 0.1491) X_69 = SYMMEDIAN POINT OF THE ANTICOMPLEMENTARY TRIANGLE (0.3185, -0.0509) X_194 = -CEVA CONJUGATE OF X(2) (0.9341, 0.2081) X_248 = -LINE CONJUGATE OF X(132) (0.6841, 0.1154) X_682 = POINT ARNEB (43.4386, -53.1959) X_694 = ISOGONAL CONJUGATE OF X(385) (1.0028, 0.0106) X_99 = STEINER POINT (0.2513, 0.2387) X_711 = EVEN (- 4, 4) CIRCUMCIRCLE POINT (0.9910, 0.0158) X_695 = ISOGONAL CONJUGATE OF X(384) (0.6916, 0.1061)
A
B
C
X384
X69
X194
X248
X682
X694
X99
X711
X695
Kimberling (6, 9, 13) | AB = 1
X695 (ISOGONAL CONJUGATE OF X384 ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a/(a^{4} + b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(1.336691646328\)
▸ Incident Central Lines4 lines
{69 194 99 711 248 682 384 694
▸ Functional Relations8 relations
Notes
Let A'B'C' be the cross-triangle of the 1st and 2nd Neuberg triangles. Let A″ be the crossdifference of B' and C' , and define B″ and C″ cyclically. The lines AA″ , BB″ , CC″ concur in X695 La be the trilinear polar of A' , and define Lb and Lc cyclically. Let A* = Lb ∩Lc , and define B* and C* cyclically. The lines AA* , BB* , CC* concur in X695 X695 ABC to A'B'C' . The reciprocal orthologic center is X4 Randy Hutson , July 31 2018)
