Can three people sit in a circle?

Solution 1:

Yes.

Mathematically, three points in space define a unique circle, so I think OP has metaphorical, mathematical and common-sense arguments that the characters can sit in a circle not just a triangle.

https://math.stackexchange.com/questions/213658/get-the-equation-of-a-circle-when-given-3-points

Solution 2:

Circle is used metaphorically to suggest a way of organizing things with no specific point being special with respect to the other points.

On a circle, all points are equal - they are equidistant from the center.

The Paris Peace Accords demonstrates this metaphor, and at the same time illustrates that an object with straight edges is a signal of conflict:

A similar debate concerned the shape of the table to be used at the conference. The North favored a circular table, in which all parties, including NLF representatives, would appear to be "equal"' in importance. The South Vietnamese argued that only a rectangular table was acceptable, for only a rectangle could show two distinct sides to the conflict.

On a circle, there is room for more, all with the same attributes of any other point. On a polygon of given number of sides, there is no room for more.

If you were to change circle to triangle, this equality would be overlooked, unless you specified equilateral triangle. This is so much more ungainly than circle that it rolls off the tongue like a spiky thorn. A triangle by itself grates almost as much.

Imagine the leader of a small wagon train (from the American West) telling the drivers to put the wagons in a triangle! It doesn't matter that there might be only three wagons - he tells them to circle the wagons!

Even when you sit at the campfire, you sit around the fire, as "in circumference, in a circle, on every side" (Etymonline.com). You can do this even if you are alone, even though, at any particular moment, you can't subtend an arc of more than a few degrees without being scorched.

Circular logic is not circular, but sometimes takes a wavering path of confusion before reaching its starting point. Yet it's still called circular.

I think you did fine using circle.

Solution 3:

Three people sat facing each other, in a circle of sorts.

This is probably how I would write it.Having said that, there is nothing wrong with your description, "a circle of three", especially in a creative writing assignment.

Your guide apparently needs to widen his/her horizons.

Just to make a case in point there is even a novel titled "Circle of Three" by Rohit Gore [http://www.goodreads.com/book/show/15990555-circle-of-three][1]