[AndrewC]

As much as I hate to use the word on this thread yet again, it is a degenerate triangle.

You can call it Bozo the Clown, but that does not make it Bozo the Clown. It is not a triangle. It is a point, and maybe a point circle, but is not a square nor a triangle. What are the angles for this point? Further are you agreeing with longshadow's argument using unit vectors of length zero?

[general_re]

It fits the definition of a triangle as long as you're willing to set aside that inconvenient triangle inequality theorem ;), and an equilateral triangle to boot - it has three equal sides of length zero. At least, it satisfies the definition for the purposes of forming a triangle circle. You can calculate the values of the angles yourself, if you like. I think you already did, actually ;)

Equilateral triangles are usually regarded as having three equal angles of 60 degrees. But that is a consequence of having three equal sides of length > 0, not a part of the definition of an equilateral triangle. Obviously, that does not hold true when the lengths are equal to zero.