You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.
You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.
|Information from Kimberling's Encyclopedia of Triangle Centers|
Trilinears cos(A + π/4) : cos(B + π/4) : cos(C + π/4)
= cos A - sin A : cos B - sin B : cos C - sin C
Barycentrics sin A cos(A + π/4) : sin B cos(B + π/4) : sin C cos(C + π/4)
X(372) is the external center of similitude of the circumcircle and the 2nd Lemoine circle (cosine circle) (Peter J. C. Moses, 5/9/03). Also, X(372) is the external center of similitude of the Gallatly circle (defined just before X(2007)) and the 1st Lemoine circle (Peter J. C. Moses, 9/10/03).
For details and references, see X(371).
X(372) lies on these lines:
2,485 3,6 4,486 25,494 193,487 315,492 601,605 602,606
X(372) = reflection of X(I) in X(J) for these (I,J): (315,639), (371,32), (638,640)
X(372) = isogonal conjugate of X(486)
X(372) = inverse-in-Brocard-circle of X(371)
X(372) = inverse-in-1st-Lemoine-circle of X(2462)
X(372) = complement of X(638)
X(372) = anticomplement of X(640)
X(372) = X(4)-Ceva conjugate of X(371)