Key Idea: Line Tangent to a Circle

A tangent line touches a circle at exactly one point and is perpendicular to the radius at that point of contact.

General Rule:

• The tangent intersects the circle at only one point.

• Its slope is the negative reciprocal of the radius’ slope at the point of tangency (perpendicular).

Why this matters for the SAT:

Tangent lines appear in geometry and coordinate problems. Knowing the perpendicular relationship to the radius allows you to find equations of tangents or solve for unknown points quickly.