X1701
EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE)
X1701 is the exsimilicenter(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, 1343 }: Central Line L(1, 1343) { 165, 1342 }: Central Line L(165, 1342) { 9, 1680 }: Central Line L(9, 1680) { 43, 1684 }: Central Line L(43, 1684) { 57, 1673 }: Central Line L(57, 1673)
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_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6155, 0.2927) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5319, 0.1548) X_9 = MITTENPUNKT (0.5110, 0.1615) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_1684 = EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.6037, 0.2733) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6607, 0.4358) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.5980, 0.2692)
A
B
C
X40
X182
X1
X1343
X165
X1342
X9
X1680
X43
X1684
X57
X1673
X1701
(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, 1343 }: Central Line L(1, 1343) { 165, 1342 }: Central Line L(165, 1342) { 9, 1680 }: Central Line L(9, 1680) { 43, 1684 }: Central Line L(43, 1684) { 57, 1673 }: Central Line L(57, 1673)
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_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6572, 0.2694) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4667, -0.0667) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5450, 0.0772) X_9 = MITTENPUNKT (0.5091, 0.1091) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5333, 0.1347) X_43 = -CEVA CONJUGATE OF X(1) (0.6941, 0.2706) X_1684 = EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.6441, 0.2470) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6500, 0.3000) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6776, 0.4070) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.6352, 0.2428)
A
B
C
X40
X182
X1
X1343
X165
X1342
X9
X1680
X43
X1684
X57
X1673
X1701
(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, 1343 }: Central Line L(1, 1343) { 165, 1342 }: Central Line L(165, 1342) { 9, 1680 }: Central Line L(9, 1680) { 43, 1684 }: Central Line L(43, 1684) { 57, 1673 }: Central Line L(57, 1673)
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_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6329, 0.2735) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4720, -0.0674) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5379, 0.0781) X_9 = MITTENPUNKT (0.5077, 0.1103) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5282, 0.1364) X_43 = -CEVA CONJUGATE OF X(1) (0.6641, 0.2739) X_1684 = EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.6216, 0.2502) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6266, 0.3045) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6508, 0.4169) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.6141, 0.2460)
A
B
C
X40
X182
X1
X1343
X165
X1342
X9
X1680
X43
X1684
X57
X1673
X1701
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, 1343 }: Central Line L(1, 1343) { 165, 1342 }: Central Line L(165, 1342) { 9, 1680 }: Central Line L(9, 1680) { 43, 1684 }: Central Line L(43, 1684) { 57, 1673 }: Central Line L(57, 1673)
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_1343 = EXSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.6662, 0.1903) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4615, -0.4096) X_1342 = INSIMILICENTER(CIRCUMCIRCLE, 1stLEMOINE CIRCLE) (0.5515, -0.1305) X_9 = MITTENPUNKT (0.5022, 0.0343) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5213, 0.0520) X_43 = -CEVA CONJUGATE OF X(1) (0.7237, 0.1860) X_1684 = EXSIMILICENTER(1st LEMOINE CIRCLE, APOLLONIUS CIRCLE) (0.6594, 0.1713) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6451, 0.2341) X_1673 = EXSIMILICENTER(INCIRCLE, 1st LEMOINE CIRCLE) (0.6434, 0.2709) X_1701 = EXSIMILICENTER(BEVAN CIRCLE, 1st LEMOINE CIRCLE) (0.6480, 0.1687)
A
B
C
X40
X182
X1
X1343
X165
X1342
X9
X1680
X43
X1684
X57
X1673
X1701
Kimberling (6, 9, 13) | AB = 1
X1701 (EXSIMILICENTER(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): \(1.032580455238\)
▸ Incident Central Lines17 lines
{1 1343 9 1680 40 182 43 1684 57 1673 165 1342 371 2017 372 2018 1571 2035 1572 2036 1672 1697 1676 1698 1677 1699 1681 1706 1683 1695 1687 1702 1688 1703
