I'm really new at this and I searched for a solution, but found nothing. I apologize if this has been covered elsewhere. I'm trying to draw some intersecting circles and compute the points where they intersect. I am having trouble with this particular function: CircleThrough.

The CircleThrough function takes a list of points and returns a Circle if it can find one.

F'rinstance:

CircleThrough[{{0,0},{1,1},{2,0}}]

gives us a Circle that crosses those three points, specifically `Circle[{{1,0}},1]

For this to return a Circle, you must have three points in the list (at least). If you include more, the function may not be able to find a Circle, and will return an error . If you supply only two points, it returns a CircleThrough object, because it can't find a unique Circle. (What to do with that CircleThrough object is another question. Maybe later.)

There is another version that takes a list of points and a center:

CircleThrough[{p1,p2,...},c}

This finds the Circle at center c, that passes through p1,p2,...

A circle is unique given it's center and one point. So, CircleThrough should give a Circle if I do this:

CircleThrough[{{0,0}},{1,0}]

It should give me the same Circle as above, but it doesn't. It just repeats what I gave it. Why? And, how do I get it to find the circle I want?

This is a simple case that shows my issue. What I want is to pick random points, and draw a couple circles that share those points, then compute the other intersections of the circles.

Any advice or ideas?