Relative Positions of a Circle and a Line
Big Idea: When we place a circle and a line on the same plane, there are exactly three possible relationships between them. The key to understanding which case we're in depends on comparing the distance from the center of the circle to the line with the radius of the circle.
Key Definitions
Distance from a point to a line ($d$): The length of the perpendicular segment drawn from the point to the line. This is always the shortest distance from the point to the line.
Radius ($r$): The distance from the center of the circle to any point on the circle.