X1700
INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE)
X1700 is the insimilicenter(Bevan circle, 1st Lemoine circle).
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, 182 }: Central Line L(40, 182) { 1, 1342 }: Central Line L(1, 1342) { 165, 1343 }: Central Line L(165, 1343) { 9, 1681 }: Central Line L(9, 1681) { 43, 1683 }: Central Line L(43, 1683) { 57, 1672 }: Central Line L(57, 1672)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_40 = BEVAN POINT (0.4286, -0.0292) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5500, 0.1846) X_1 = INCENTER (0.5714, 0.2333) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5004, 0.1824) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1683 = INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5110, 0.1202) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5619, 0.2116) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5232, 0.1374)
A
B
C
X40
X182
X1
X1342
X165
X1343
X9
X1681
X43
X1683
X57
X1672
X1700
(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, 182 }: Central Line L(40, 182) { 1, 1342 }: Central Line L(1, 1342) { 165, 1343 }: Central Line L(165, 1343) { 9, 1681 }: Central Line L(9, 1681) { 43, 1683 }: Central Line L(43, 1683) { 57, 1672 }: Central Line L(57, 1672)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_40 = BEVAN POINT (0.4000, -0.2000) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5700, 0.1200) X_1 = INCENTER (0.6000, 0.2000) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5450, 0.0772) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4667, -0.0667) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6572, 0.2694) X_9 = MITTENPUNKT (0.5091, 0.1091) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4918, 0.1513) X_43 = -CEVA CONJUGATE OF X(1) (0.6941, 0.2706) X_1683 = INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5153, 0.0261) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6500, 0.3000) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5874, 0.1665) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5331, 0.0505)
A
B
C
X40
X182
X1
X1342
X165
X1343
X9
X1681
X43
X1683
X57
X1672
X1700
(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, 182 }: Central Line L(40, 182) { 1, 1342 }: Central Line L(1, 1342) { 165, 1343 }: Central Line L(165, 1343) { 9, 1681 }: Central Line L(9, 1681) { 43, 1683 }: Central Line L(43, 1683) { 57, 1672 }: Central Line L(57, 1672)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_40 = BEVAN POINT (0.4159, -0.2021) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5590, 0.1215) X_1 = INCENTER (0.5841, 0.2021) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5379, 0.0781) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4720, -0.0674) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6329, 0.2735) X_9 = MITTENPUNKT (0.5077, 0.1103) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4930, 0.1536) X_43 = -CEVA CONJUGATE OF X(1) (0.6641, 0.2739) X_1683 = INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5129, 0.0266) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6266, 0.3045) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.5735, 0.1681) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5279, 0.0511)
A
B
C
X40
X182
X1
X1342
X165
X1343
X9
X1681
X43
X1683
X57
X1672
X1700
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, 182 }: Central Line L(40, 182) { 1, 1342 }: Central Line L(1, 1342) { 165, 1343 }: Central Line L(165, 1343) { 9, 1681 }: Central Line L(9, 1681) { 43, 1683 }: Central Line L(43, 1683) { 57, 1672 }: Central Line L(57, 1672)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_40 = BEVAN POINT (0.3846, -0.6794) X_182 = MIDPOINT OF BROCARD DIAMETER (0.5787, -0.0546) X_1 = INCENTER (0.6154, 0.1300) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5515, -0.1305) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4615, -0.4096) X_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6662, 0.1903) X_9 = MITTENPUNKT (0.5022, 0.0343) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4896, 0.1108) X_43 = -CEVA CONJUGATE OF X(1) (0.7237, 0.1860) X_1683 = INSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.5168, -0.2276) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6451, 0.2341) X_1672 = INSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6043, 0.0743) X_1700 = INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5382, -0.1848)
A
B
C
X40
X182
X1
X1342
X165
X1343
X9
X1681
X43
X1683
X57
X1672
X1700
Kimberling (6, 9, 13) | AB = 1
X1700 (INSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE 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 \(f(A,B,C) = 2 \cos(A - \omega ) + \cos A - \cos B - \cos C + 1\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(5.552444214923\)
▸ Incident Central Lines17 lines
{1 1342 9 1681 40 182 43 1683 57 1672 165 1343 371 2018 372 2017 1571 2036 1572 2035 1673 1697 1676 1699 1677 1698 1680 1706 1684 1695 1687 1703 1688 1702
