If you call a tangent a line touching a circle at one point, and a secant two...

The Blade Dancer

Is there anything you call a line that touches a circle at 3 or more points? If you have a line directly on one part of the circumference, do you have a line touching the circle at more than 2 points?

debbie

@the-blade-dancer That's interesting. Actually, I do believe it's not possible for a straight line to intersect a circle at three points, though a curve or a shape definitely could. A triangle could intersect a circle at three points. And if two circles are the same size and lie right on top of each other, I suppose you could say they intersect at \(\infty\) infinitely-many points!

energizedpanda

@the-blade-dancer I suppose you can prove this with coordinate bashing, that it is impossible for a line to touch a circle at more than 2 points.