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Its true...i didnt look it up

It is TRUE.

that is the formula for it , look in your book

@experimentX its the formula for it man

formula is just expression of logic.

yeah

I left out the word "or"

or an ellipse

if you let r=0 then you will destroy properties that all 'normal' circles have

I would call it a degenerate circle

I like "degenerate."

It's a shorter way of saying "circle with radius zero."

true so true........

that depends on what definition you use

that way all my theorems hold and make sense

draw a tangent to a circle with radius zero

And even if there is no single unique tangent to that point, a tangent can still be drawn.

Those are properties of some circles, but are they included in the definition of "circle?"

Argument from personal preference isn't valid, I'd think.

most are theorems that require that a circle have an interior