TITLE: Smallest Circumcircle of Three Triangles
QUESTION [10 upvotes]: What is the minimum diameter of the circumcircle about the triangle formed by the center points of three congruent equilateral triangles that do not overlap?
The diagram is the best solution I've found so far.  If the triangles have a side of length 1, the circle has diameter 0.853.

REPLY [3 votes]: This is minimal. The tangent line is parallel to the edge of the triangle.
Diameter of circle is $\frac{10\sqrt{3}-6\sqrt{6}}{3}\approx0.8745232$