# Are similar circles really a thing?

I'm a fifteen year old who is currently studying circle geometry (if that is the appropriate term) and our teacher stated that concentric circles are similar. I thought about this, and it doesn't make sense to me. The reason is because of proportionality. For example, similar triangles are similar because they have the same angles and they have proportional sides. However, circles can not be compared for angles, so that's out (as they all have the same 360 degree angle at the center) and the only factor is their size, which is directly influenced by their radius. If the radius is the only variable involved in a triangle like this, how can a circle be NOT proportional to another circle? If a case of that existed, there would be meaning (at least from my current perspective) to the term "similar circle."

Help and critique on my logic is requested, and an explanation as to the term "similar circle."

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Concentric circles are similar. So are non-concentric circles. – André Nicolas Mar 4 at 5:06
But what is the point of the term "similar circle" if there are no cases of "non similar circles"? I'm really confused about this topic. – Gil Keidar Mar 4 at 5:07
In a proof, one might be using the fact that (any) two circles are similar, so it may be useful to mention it. – André Nicolas Mar 4 at 5:09
You are right, in Euclidean geometry all circles are similar. Likewise, all parabolas are similar. – bof Mar 4 at 5:10
"similar" does not only refer to circles. It refers to geometric shapes. For example, it doesn't make so much sense to speak of a rectangular square although a square is always rectangular. – Friedrich Philipp Mar 4 at 5:12