X1695
INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE)
The exsimilicenter of the Bevan and Apollonius circles is
X43 .
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) { 40, 43 }: Central Line L(40, 43) { 165, 386 }: Central Line L(165, 386) { 1, 573 }: Central Line L(1, 573) { 10, 962 }: Central Line L(10, 962) { 57, 1682 }: Central Line L(57, 1682) { 181, 1697 }: Central Line L(181, 1697)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_939 = ISOGONAL CONJUGATE OF X(938) (0.5573, 0.2204) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5490, 0.1921) X_40 = BEVAN POINT (0.4286, -0.0292) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.5912, 0.2526) X_1 = INCENTER (0.5714, 0.2333) X_573 = ORTHOHARMONIC OF X(58) (0.4583, 0.2009) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_962 = LONGUET-HIGGINS POINT (0.7551, 0.6582) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5367, 0.1744) X_181 = APOLLONIUS POINT (0.6163, 0.3093) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5449, 0.1845) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3697, -0.1216)
A
B
C
X939
X55
X40
X43
X165
X386
X1
X573
X10
X962
X57
X1682
X181
X1697
X1695
(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) { 40, 43 }: Central Line L(40, 43) { 165, 386 }: Central Line L(165, 386) { 1, 573 }: Central Line L(1, 573) { 10, 962 }: Central Line L(10, 962) { 57, 1682 }: Central Line L(57, 1682) { 181, 1697 }: Central Line L(181, 1697)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_939 = ISOGONAL CONJUGATE OF X(938) (0.5803, 0.1865) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5714, 0.1429) X_40 = BEVAN POINT (0.4000, -0.2000) X_43 = -CEVA CONJUGATE OF X(1) (0.6941, 0.2706) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4667, -0.0667) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.6296, 0.2222) X_1 = INCENTER (0.6000, 0.2000) X_573 = ORTHOHARMONIC OF X(58) (0.6632, 0.0000) X_10 = SPIEKER CENTER (0.5200, 0.1400) X_962 = LONGUET-HIGGINS POINT (0.8400, 0.8800) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6500, 0.3000) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5561, 0.1220) X_181 = APOLLONIUS POINT (0.6545, 0.2970) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5667, 0.1333) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3123, -0.3404)
A
B
C
X939
X55
X40
X43
X165
X386
X1
X573
X10
X962
X57
X1682
X181
X1697
X1695
(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) { 40, 43 }: Central Line L(40, 43) { 165, 386 }: Central Line L(165, 386) { 1, 573 }: Central Line L(1, 573) { 10, 962 }: Central Line L(10, 962) { 57, 1682 }: Central Line L(57, 1682) { 181, 1697 }: Central Line L(181, 1697)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_939 = ISOGONAL CONJUGATE OF X(938) (0.5675, 0.1885) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5599, 0.1439) X_40 = BEVAN POINT (0.4159, -0.2021) X_43 = -CEVA CONJUGATE OF X(1) (0.6641, 0.2739) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4720, -0.0674) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.6091, 0.2246) X_1 = INCENTER (0.5841, 0.2021) X_573 = ORTHOHARMONIC OF X(58) (0.3890, 0.0000) X_10 = SPIEKER CENTER (0.5170, 0.1419) X_962 = LONGUET-HIGGINS POINT (0.7862, 0.8901) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6266, 0.3045) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5468, 0.1225) X_181 = APOLLONIUS POINT (0.6305, 0.3013) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5558, 0.1341) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.3427, -0.3427)
A
B
C
X939
X55
X40
X43
X165
X386
X1
X573
X10
X962
X57
X1682
X181
X1697
X1695
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) { 40, 43 }: Central Line L(40, 43) { 165, 386 }: Central Line L(165, 386) { 1, 573 }: Central Line L(1, 573) { 10, 962 }: Central Line L(10, 962) { 57, 1682 }: Central Line L(57, 1682) { 181, 1697 }: Central Line L(181, 1697)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_939 = ISOGONAL CONJUGATE OF X(938) (0.6011, 0.1233) X_55 = INSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.5940, 0.0549) X_40 = BEVAN POINT (0.3846, -0.6794) X_43 = -CEVA CONJUGATE OF X(1) (0.7237, 0.1860) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4615, -0.4096) X_386 = INVERSE-IN-BROCARD-CIRCLE OF X(58) (0.6513, 0.1486) X_1 = INCENTER (0.6154, 0.1300) X_573 = ORTHOHARMONIC OF X(58) (0.6395, 0.0705) X_10 = SPIEKER CENTER (0.5089, 0.0750) X_962 = LONGUET-HIGGINS POINT (0.8639, 1.6388) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6451, 0.2341) X_1682 = INSIMILICENTER(INCIRCLE, APOLLONIUS CIRCLE) (0.5847, 0.0398) X_181 = APOLLONIUS POINT (0.6498, 0.2312) X_1697 = INSIMILICENTER(BEVAN CIRCLE, INCIRCLE) (0.5918, 0.0472) X_1695 = INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) (0.2729, -0.9645)
A
B
C
X939
X55
X40
X43
X165
X386
X1
X573
X10
X962
X57
X1682
X181
X1697
X1695
Kimberling (6, 9, 13) | AB = 1
X1695 (INSIMILICENTER(BEVAN CIRCLE, APOLLONIUS CIRCLE) ) 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 \(f(a,b,c) = r(r^{2} + s^{2}) + 4Rs(r \sin A - s \cos A)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(15.702433290861\)
▸ Incident Central Lines15 lines
{1 573 10 962 40 43 57 1682 165 386 181 1697 978 1764 1683 1701 1684 1700 1685 1703 1686 1702 1693 1705 1694 1704 2017 2020 2018 2019
▸ Functional Relations1 relation
