X2940
EXCENTRAL-ISOGONAL CONJUGATE OF X5
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) { 35, 37 }: Central Line L(35, 37) { 191, 210 }: Central Line L(191, 210) { 484, 1046 }: Central Line L(484, 1046) { 40, 2948 }: Central Line L(40, 2948)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5373, 0.1706) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5567, 0.2158) X_191 = -CEVA CONJUGATE OF X(1) (0.4859, 0.1209) X_210 = -CEVA CONJUGATE OF X(37) (0.4925, 0.1466) X_484 = 1st EVANS PERSPECTOR (2.0952, 3.0327) X_1046 = -CEVA CONJUGATE OF X(1) (0.6500, 0.3366) X_40 = BEVAN POINT (0.4286, -0.0292) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (-0.0682, 0.8624) X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X(5) (0.4415, -0.0524)
A
B
C
X5
X35
X37
X191
X210
X484
X1046
X40
X2948
X2940
(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) { 35, 37 }: Central Line L(35, 37) { 191, 210 }: Central Line L(191, 210) { 484, 1046 }: Central Line L(484, 1046) { 40, 2948 }: Central Line L(40, 2948)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_5 = NINE-POINT CENTER (0.5700, 0.2400) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5556, 0.1111) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5787, 0.1787) X_191 = -CEVA CONJUGATE OF X(1) (0.4737, 0.0526) X_210 = -CEVA CONJUGATE OF X(37) (0.4800, 0.0933) X_484 = 1st EVANS PERSPECTOR (1.4000, 1.8000) X_1046 = -CEVA CONJUGATE OF X(1) (0.7043, 0.3217) X_40 = BEVAN POINT (0.4000, -0.2000) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (0.1200, 0.7600) X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X(5) (0.4225, -0.2772)
A
B
C
X5
X35
X37
X191
X210
X484
X1046
X40
X2948
X2940
(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) { 35, 37 }: Central Line L(35, 37) { 191, 210 }: Central Line L(191, 210) { 484, 1046 }: Central Line L(484, 1046) { 40, 2948 }: Central Line L(40, 2948)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_5 = NINE-POINT CENTER (0.5590, 0.2429) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5465, 0.1118) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5661, 0.1805) X_191 = -CEVA CONJUGATE OF X(1) (0.4779, 0.0531) X_210 = -CEVA CONJUGATE OF X(37) (0.4833, 0.0946) X_484 = 1st EVANS PERSPECTOR (1.2932, 1.9071) X_1046 = -CEVA CONJUGATE OF X(1) (0.6730, 0.3270) X_40 = BEVAN POINT (0.4159, -0.2021) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (0.1799, 0.7696) X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X(5) (0.4348, -0.2798)
A
B
C
X5
X35
X37
X191
X210
X484
X1046
X40
X2948
X2940
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) { 35, 37 }: Central Line L(35, 37) { 191, 210 }: Central Line L(191, 210) { 484, 1046 }: Central Line L(484, 1046) { 40, 2948 }: Central Line L(40, 2948)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_5 = NINE-POINT CENTER (0.5666, 0.2774) X_35 = {X(1),X(3)}-HARMONIC CONJUGATE OF X(36) (0.5793, 0.0033) X_37 = CROSSPOINT OF INCENTER AND CENTROID (0.5913, 0.1097) X_191 = -CEVA CONJUGATE OF X(1) (0.4617, -0.0404) X_210 = -CEVA CONJUGATE OF X(37) (0.4646, 0.0259) X_484 = 1st EVANS PERSPECTOR (0.8087, 0.8081) X_1046 = -CEVA CONJUGATE OF X(1) (0.7124, 0.2376) X_40 = BEVAN POINT (0.3846, -0.6794) X_2948 = EXCENTRAL-ISOGONAL CONJUGATE OF X(30) (0.3795, 0.4616) X_2940 = EXCENTRAL-ISOGONAL CONJUGATE OF X(5) (0.3891, -1.6777)
A
B
C
X5
X35
X37
X191
X210
X484
X1046
X40
X2948
X2940
Kimberling (6, 9, 13) | AB = 1
X2940 (EXCENTRAL-ISOGONAL CONJUGATE OF X5 ) 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) is as described just before
X2883 Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(22.155687724165\)
▸ Incident Central Lines4 lines
▸ Functional Relations1 relation
Notes
Let Oa be the A-extraversion of the Conway circle (the circle centered at the A -excenter and passing through A , with radius \(\sqrt{r_a^{2} + s^{2}}\) , where r_a is the A-exradius). Let A″ be the intersection, other than A, of the circumcircle and Oa ; define B″ and C″ cyclically. The triangle A″B″C″ is perspective to the excentral triangle at X2940 Randy Hutson , April 9, 2016)
