X2014
EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE)
X2014 is the exsimilicenter(gallatly circle, Spieker 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) { 10, 39 }: Central Line L(10, 39) { 2, 2007 }: Central Line L(2, 2007) { 8, 2008 }: Central Line L(8, 2008) { 371, 1680 }: Central Line L(371, 1680) { 372, 1681 }: Central Line L(372, 1681) { 958, 1690 }: Central Line L(958, 1690)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_2 = CENTROID (0.5374, 0.2000) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5746, 0.2319) X_8 = NAGEL POINT (0.4694, 0.1333) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.3669, 0.3221) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5289, 0.1837) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5004, 0.1824) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5529, 0.1894) X_2014 = EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.4664, 0.1388)
A
B
C
X10
X39
X2
X2007
X8
X2008
X371
X1680
X372
X1681
X958
X1690
X2014
(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) { 10, 39 }: Central Line L(10, 39) { 2, 2007 }: Central Line L(2, 2007) { 8, 2008 }: Central Line L(8, 2008) { 371, 1680 }: Central Line L(371, 1680) { 372, 1681 }: Central Line L(372, 1681) { 958, 1690 }: Central Line L(958, 1690)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_10 = SPIEKER CENTER (0.5200, 0.1400) X_39 = BROCARD MIDPOINT (0.6138, 0.1951) X_2 = CENTROID (0.5467, 0.1600) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.6066, 0.1976) X_8 = NAGEL POINT (0.4400, 0.0800) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.4315, 0.2604) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5946, 0.1622) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5333, 0.1347) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7692, 0.4615) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4918, 0.1513) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5167, 0.1167) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5794, 0.1361) X_2014 = EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.4394, 0.0927)
A
B
C
X10
X39
X2
X2007
X8
X2008
X371
X1680
X372
X1681
X958
X1690
X2014
(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) { 10, 39 }: Central Line L(10, 39) { 2, 2007 }: Central Line L(2, 2007) { 8, 2008 }: Central Line L(8, 2008) { 371, 1680 }: Central Line L(371, 1680) { 372, 1681 }: Central Line L(372, 1681) { 958, 1690 }: Central Line L(958, 1690)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_10 = SPIEKER CENTER (0.5170, 0.1419) X_39 = BROCARD MIDPOINT (0.5955, 0.1965) X_2 = CENTROID (0.5393, 0.1620) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5896, 0.1994) X_8 = NAGEL POINT (0.4499, 0.0817) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.4433, 0.2705) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5794, 0.1635) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5282, 0.1364) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7296, 0.4725) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4930, 0.1536) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5141, 0.1180) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.5665, 0.1368) X_2014 = EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.4495, 0.0949)
A
B
C
X10
X39
X2
X2007
X8
X2008
X371
X1680
X372
X1681
X958
X1690
X2014
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) { 10, 39 }: Central Line L(10, 39) { 2, 2007 }: Central Line L(2, 2007) { 8, 2008 }: Central Line L(8, 2008) { 371, 1680 }: Central Line L(371, 1680) { 372, 1681 }: Central Line L(372, 1681) { 958, 1690 }: Central Line L(958, 1690)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_10 = SPIEKER CENTER (0.5089, 0.0750) X_39 = BROCARD MIDPOINT (0.6418, 0.1220) X_2 = CENTROID (0.5444, 0.0934) X_2007 = INSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.6265, 0.1267) X_8 = NAGEL POINT (0.4024, 0.0200) X_2008 = EXSIMILICENTER(GALLATLY CIRCLE, INCIRCLE) (0.5456, 0.1511) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.6182, 0.0560) X_1680 = INSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.5213, 0.0520) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7352, 0.3832) X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4896, 0.1108) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5080, 0.0392) X_1690 = INVERSE-IN-BROCARD-CIRCLE OF X(1688) (0.6079, 0.0272) X_2014 = EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER CIRCLE) (0.4332, 0.0483)
A
B
C
X10
X39
X2
X2007
X8
X2008
X371
X1680
X372
X1681
X958
X1690
X2014
Kimberling (6, 9, 13) | AB = 1
X2014 (EXSIMILICENTER(GALLATLY CIRCLE, SPIEKER 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 \(f(A,B,C) = [\sin B + \sin C - \sin A \sin(A + \omega )](\csc A)\)
Barycentrics: \((\sin A)f(A,B,C) : (\sin B)f(B,C,A) : (\sin C)f(C,A,B)\)
Search Value (6, 9, 13): \(3.972132470618\)
▸ Incident Central Lines14 lines
{2 2007 8 2008 9 2017 10 39 371 1680 372 1681 958 1690 1329 2010 1376 1689 1377 1671 1378 1670 1678 2011 1679 2012 1706 2018
