> Equal length would make it correct, I think.

And the three lines of equal length should go to different points on the edge of the circle as well. Three lines from a point to the same position on the edge wouldn't work - but perhaps I'm mathematically paranoid now :-)

Well they wouldn't really be three lines if they all go from the same point to the same other point. They would all be the same line.

Unless the language of math does allow "references" like programming languages.

All you need is to require three different lines of equal length.

But I don't see the significance of calling this a theorem. It seems perfectly obvious and elementary and almost just the definition of a circle.

> Well they wouldn't really be three lines if they all go from the same point to the same other point. They would all be the same line.

> Unless the language of math does allow "references" like programming languages.

Ha, that indicates that I'm clearly thinking more as a programmer than as a mathematician :-) Thanks.

The definition of a circle is literally the set of all points whose distance from a point P is r, so yeah, I'm in agreement.

EDIT: in a plane

The lines being tangent to the circle would also work.

Nope, you can have two equal lines extending from a non-central point. Connecting the points would give you an isosceles triangle.

As well as hitting the edge of the circle at right angles.