# A simple Circle Proof

• Feb 2nd 2010, 11:12 AM
GreenDay14
A simple Circle Proof
I have a question here that says: A straight line cannot cut a circle at more than two points.

Obviously a straight line cannot cut at more than two points, because it can only:
i) not hit the circle at all
ii)be a tangent to the circle (only hit at once point)
iii)or go right through the circle and intersect at two points.

I assume this question is to be solved using a contradiction but I can not figure out how to write our a proof for this one.

Any help would be greatly appreciated. Thanks a lot.
• Feb 2nd 2010, 11:24 AM
HallsofIvy
Quote:

Originally Posted by GreenDay14
I have a question here that says: A straight line cannot cut a circle at more than two points.

Obviously a straight line cannot cut at more than two points, because it can only:
i) not hit the circle at all
ii)be a tangent to the circle (only hit at once point)
iii)or go right through the circle and intersect at two points.

I assume this question is to be solved using a contradiction but I can not figure out how to write our a proof for this one.

Any help would be greatly appreciated. Thanks a lot.

Well, what do you have to use? Is this a basic geometry course and you are to use the postulates of Euclidean Geometry? Is so, what postulates do you know that have to do with circles? (Exactly how postulates are stated will differ from course to course and we do not know how they are given in your course.) Can you use Cartesian coordinates? If so, then how can you write equations for a general circle and line?