X1378
EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE)
X1378 is the exsimilicenter(2nd Lemoine 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) { 6, 10 }: Central Line L(6, 10) { 2, 1124 }: Central Line L(2, 1124) { 371, 958 }: Central Line L(371, 958) { 8, 1335 }: Central Line L(8, 1335) { 372, 1376 }: Central Line L(372, 1376) { 486, 1329 }: Central Line L(486, 1329)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_2 = CENTROID (0.5374, 0.2000) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5846, 0.2489) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5652, 0.2097) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5166, 0.1682) X_8 = NAGEL POINT (0.4694, 0.1333) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4024, 0.0326) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7148, 0.4568) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5265, 0.2074) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4903, 0.1280) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4609, 0.1206)
A
B
C
X6
X10
X2
X1124
X371
X958
X8
X1335
X372
X1376
X486
X1329
X1378
(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) { 6, 10 }: Central Line L(6, 10) { 2, 1124 }: Central Line L(2, 1124) { 371, 958 }: Central Line L(371, 958) { 8, 1335 }: Fuhrmann Line { 372, 1376 }: Central Line L(372, 1376) { 486, 1329 }: Central Line L(486, 1329)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_10 = SPIEKER CENTER (0.5200, 0.1400) X_2 = CENTROID (0.5467, 0.1600) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6182, 0.2182) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5946, 0.1622) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5167, 0.1167) X_8 = NAGEL POINT (0.4400, 0.0800) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4000, 0.0000) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7692, 0.4615) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5250, 0.1750) X_486 = INNER VECTEN POINT (2.3200, 0.2400) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4867, 0.0733) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4343, 0.0686)
A
B
C
X6
X10
X2
X1124
X371
X958
X8
X1335
X372
X1376
X486
X1329
X1378
(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) { 6, 10 }: Central Line L(6, 10) { 2, 1124 }: Central Line L(2, 1124) { 371, 958 }: Central Line L(371, 958) { 8, 1335 }: Fuhrmann Line { 372, 1376 }: Central Line L(372, 1376) { 486, 1329 }: Central Line L(486, 1329)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_10 = SPIEKER CENTER (0.5170, 0.1419) X_2 = CENTROID (0.5393, 0.1620) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.5995, 0.2206) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.5794, 0.1635) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5141, 0.1180) X_8 = NAGEL POINT (0.4499, 0.0817) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.4159, 0.0000) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7296, 0.4725) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5213, 0.1778) X_486 = INNER VECTEN POINT (2.6471, 0.2429) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4885, 0.0733) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4450, 0.0699)
A
B
C
X6
X10
X2
X1124
X371
X958
X8
X1335
X372
X1376
X486
X1329
X1378
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) { 6, 10 }: Central Line L(6, 10) { 2, 1124 }: Central Line L(2, 1124) { 371, 958 }: Central Line L(371, 958) { 8, 1335 }: Central Line L(8, 1335) { 372, 1376 }: Central Line L(372, 1376) { 486, 1329 }: Central Line L(486, 1329)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_10 = SPIEKER CENTER (0.5089, 0.0750) X_2 = CENTROID (0.5444, 0.0934) X_1124 = ISOGONAL CONJUGATE OF X(1123) (0.6325, 0.1445) X_371 = KENMOTU POINT (CONGRUENT SQUARES POINT) (0.6182, 0.0560) X_958 = INTERSECTION OF LINES X(1)X(6) AND X(2)X(12) (0.5080, 0.0392) X_8 = NAGEL POINT (0.4024, 0.0200) X_1335 = {X(1),X(6)}-HARMONIC CONJUGATE OF X(1124) (0.5226, 0.0516) X_372 = {X(3),X(6)}-HARMONIC CONJUGATE OF X(371) (0.7352, 0.3832) X_1376 = EXSIMILICENTER(CIRCUMCIRCLE, SPIEKER CIRCLE) (0.5100, 0.1200) X_486 = INNER VECTEN POINT (0.8351, -0.0536) X_1329 = COMPLEMENTARY CONJUGATE OF X(1) (0.4918, 0.0153) X_1378 = EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) (0.4309, 0.0275)
A
B
C
X6
X10
X2
X1124
X371
X958
X8
X1335
X372
X1376
X486
X1329
X1378
Kimberling (6, 9, 13) | AB = 1
X1378 (EXSIMILICENTER(2nd LEMOINE CIRCLE, SPIEKER CIRCLE) ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(bc(b + c - a \sin A) : :\)
Search Value (6, 9, 13): \(4.204836868852\)
▸ Linear Combinations1 combination
▸ Incident Central Lines7 lines
{2 1124 6 10 8 1335 371 958 372 1376 486 1329 993 1151
▸ Functional Relations1 relation
