Three equilateral triangles with side lengths 28 are placed in the position as shown in the picture above. All the contacts are perfect and a circle passes by exactly one vertex per triangle. What’s the minimal radius?
So I believe the radius is:
I get this by assuming that the centre of the circle is $x$ along the line between the two joined triangles on the right, and that the apex of the triangle on the left is horizontal with this, which I think is correct. Solve for $x$ here. And substitute back to get the radius here.