a line and a circle can have at most two common points Solution True. The simplest proof that I can think of is - We can draw a perpendicular bisector of a chord that goes through the center of the circle. If there were three points on the same chord, the bisectors would be parallel and two of them would miss the center Hence, a line and a circle can have at most two common points.

1. a line and a circle can have at most two common points
Solution
True. The simplest proof that I can think of is - We can draw a perpendicular bisector of a chord
that goes through the center of the circle. If there were three points on the same chord, the
bisectors would be parallel and two of them would miss the center
Hence, a line and a circle can have at most two common points