X1505
EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES
X1505 is the exsimilicenter of moses and 2nd Lemoine circles.
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) { 3, 6 }: Brocard Axis { 2, 589 }: Central Line L(2, 589) { 115, 486 }: Central Line L(115, 486) { 394, 494 }: Central Line L(394, 494) { 492, 626 }: Central Line L(492, 626) { 615, 640 }: Central Line L(615, 640)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1307 = COLLINGS TRANSFORM OF X(640) (0.2010, -0.3115) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0394, -0.1040) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_2 = CENTROID (0.5374, 0.2000) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (0.6340, 0.4099) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7507, 0.0838) X_486 = INNER VECTEN POINT (-0.0810, -0.0170) X_394 = -CEVA CONJUGATE OF X(3) (0.3778, 0.0284) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (3.0897, 0.6637) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4893, 0.1483) X_626 = COMPLEMENT OF X(32) (0.4861, 0.1333) X_615 = ISOGONAL CONJUGATE OF X(589) (0.4337, 0.0885) X_640 = COMPLEMENT OF X(372) (0.4487, 0.0715) X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES (0.4682, 0.0496)
A
B
C
X1307
X512
X3
X6
X2
X589
X115
X486
X394
X494
X492
X626
X615
X640
X1505
(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) { 3, 6 }: Brocard Axis { 2, 589 }: Central Line L(2, 589) { 115, 486 }: Central Line L(115, 486) { 394, 494 }: Central Line L(394, 494) { 492, 626 }: Central Line L(492, 626) { 615, 640 }: Central Line L(615, 640)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_1307 = COLLINGS TRANSFORM OF X(640) (0.2404, -0.4273) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0433, -0.1297) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_2 = CENTROID (0.5467, 0.1600) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (0.6250, 0.5357) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7445, 0.0609) X_486 = INNER VECTEN POINT (2.3200, 0.2400) X_394 = -CEVA CONJUGATE OF X(3) (0.3600, 0.0000) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (1.7895, 0.3158) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4702, 0.0944) X_626 = COMPLEMENT OF X(32) (0.4790, 0.0841) X_615 = ISOGONAL CONJUGATE OF X(589) (0.3345, -0.0218) X_640 = COMPLEMENT OF X(372) (0.4354, 0.0092) X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES (0.5207, 0.0355)
A
B
C
X1307
X512
X3
X6
X2
X589
X115
X486
X394
X494
X492
X626
X615
X640
X1505
(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) { 3, 6 }: Brocard Axis { 2, 589 }: Central Line L(2, 589) { 115, 486 }: Central Line L(115, 486) { 394, 494 }: Central Line L(394, 494) { 492, 626 }: Central Line L(492, 626) { 615, 640 }: Central Line L(615, 640)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_1307 = COLLINGS TRANSFORM OF X(640) (0.2764, -0.4472) X_512 = ISOGONAL CONJUGATE OF X(99) (1.0565, -0.0893) X_3 = CIRCUMCENTER (0.5000, 0.0000) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_2 = CENTROID (0.5393, 0.1620) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (0.6099, 0.5211) X_115 = CENTER OF KIEPERT HYPERBOLA (0.7135, 0.0464) X_486 = INNER VECTEN POINT (2.6471, 0.2429) X_394 = -CEVA CONJUGATE OF X(3) (0.3820, 0.0000) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (1.9960, 0.3209) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4753, 0.0961) X_626 = COMPLEMENT OF X(32) (0.4818, 0.0839) X_615 = ISOGONAL CONJUGATE OF X(589) (0.3674, -0.0150) X_640 = COMPLEMENT OF X(372) (0.4442, 0.0067) X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES (0.5126, 0.0260)
A
B
C
X1307
X512
X3
X6
X2
X589
X115
X486
X394
X494
X492
X626
X615
X640
X1505
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) { 3, 6 }: Brocard Axis { 2, 589 }: Central Line L(2, 589) { 115, 486 }: Central Line L(115, 486) { 394, 494 }: Central Line L(394, 494) { 492, 626 }: Central Line L(492, 626) { 615, 640 }: Central Line L(615, 640)
A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_1307 = COLLINGS TRANSFORM OF X(640) (-0.0624, -0.3705) X_512 = ISOGONAL CONJUGATE OF X(99) (1.1621, -0.1275) X_3 = CIRCUMCENTER (0.5000, -0.2747) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_2 = CENTROID (0.5444, 0.0934) X_589 = 2nd KENMOTU-VAN LAMOEN POINT (1.0516, -0.1490) X_115 = CENTER OF KIEPERT HYPERBOLA (0.6909, 0.0207) X_486 = INNER VECTEN POINT (0.8351, -0.0536) X_394 = -CEVA CONJUGATE OF X(3) (0.4580, 0.0382) X_494 = 2nd VAN LAMOEN HOMOTHETIC CENTER (5.3259, 0.6306) X_492 = CEVAPOINT OF X(2) AND X(488) (0.4310, 0.0210) X_626 = COMPLEMENT OF X(32) (0.4782, 0.0302) X_615 = ISOGONAL CONJUGATE OF X(589) (16.4739, 10.2653) X_640 = COMPLEMENT OF X(372) (0.4490, -0.0516) X_1505 = EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES (0.6188, 0.0578)
A
B
C
X1307
X512
X3
X6
X2
X589
X115
X486
X394
X494
X492
X626
X615
X640
X1505
Kimberling (6, 9, 13) | AB = 1
X1505 (EXSIMILICENTER OF MOSES AND 2nd LEMOINE CIRCLES ) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\) .
Trilinears: \(a[b^{2} + c^{2} - 4(\operatorname{area} ABC)]\)
Search Value (6, 9, 13): \(2.409751547180\)
▸ Alternate Coordinates2 forms
Trilinears: \(2 \sin A \sin \omega - \sin(A + \omega )\) (Peter J. C. Moses, 9/12/03)
Trilinears: \(\cos A + (\sin A)(- 2 + \cot \omega )\) (Peter J. C. Moses, 9/12/03)
▸ Linear Combinations1 combination
▸ Incident Central Lines9 lines
{2 589 3 6 115 486 394 494 485 1508 492 626 615 640 1015 1335 1124 1500
▸ Functional Relations6 relations
