Relative positions of a line and a circle

Given a line $r$ and a circle $\gamma$, three possibilities arise:

• $r$ is external to $\gamma$: no point in common.
• $r$ is tangent to $\gamma$: a single point in common (counted with multiplicity).
• $r$ is secant to $\gamma$: two distinct points in common.

The three relative positions of a line with respect to a circle: external, tangent and secant.

Mnemonic rule: distance $d(C,r)$ greater than, equal to or less than the radius $R$ $\iff$ external, tangent or secant line.

Links

Topics: Analytical circle
Concepts: Line-circle intersection · Line · External line · Secant line · Tangent line
Skills: Analytical geometry