Detailed definition
Understanding Tangent
A tangent to a circle touches the circle at exactly one point, called the point of tangency. At that point, the radius drawn to the contact point is perpendicular to the tangent line.
Tangents are important because they turn circle vocabulary into theorem language. They appear in construction work, in tangent-chord angle problems, and in arguments about equal tangent segments from an external point.
This page keeps the radius and the touch point on the screen together so the defining geometry of tangency stays visible instead of being inferred loosely.
Key facts
Important ideas to remember
- A tangent touches a circle at exactly one point.
- A tangent and the radius to the point of tangency meet at a right angle.
- A tangent touches the circle at one point, whereas a secant cuts through at two points.
- Tangency is a local contact condition, not simply a line that passes near the circle's edge.
Where it is used
Where tangent shows up
- Use tangents in compass-and-straightedge constructions and formal geometry proofs.
- Use them in tangent-chord angle problems and in right-angle relationships at the circle boundary.
- Use them when modelling contact paths such as wheels touching a surface or external support lines.
Common mistakes
What to watch out for
- Do not label a line as tangent if it intersects the circle in two places, even if the second cut looks small.
- Do not forget the perpendicular radius fact at the point of tangency.
- Do not place the point of tangency away from the actual contact point on the boundary.