Circle lines and segments: radius, chord, diameter, secant, tangent

Expert intro: These circle vocabulary questions are about precision. The names sound similar, but each one describes a different geometric relationship to the circle.

Detailed walkthrough

Here are the definitions of each term:

Radius

A radius is a line segment from the center of the circle to a point on the circle.

Chord

A chord is a line segment with both endpoints on the circle.

Diameter

A diameter is a chord that passes through the center of the circle. It is the longest chord.

Secant

A secant is a line that intersects the circle at exactly two points.

Tangent

A tangent is a line that touches the circle at exactly one point.

Handy relationship

The diameter is twice the radius:

$d=2r$

💡 Pitfall guide

A common mix-up is calling any segment inside the circle a chord. That is only true if both endpoints lie on the circle. Also, a tangent touches the circle once; it does not cut through it.

🔄 Real-world variant

If the line touches the circle at one point and is perpendicular to the radius at that point, that relationship identifies a tangent. If a segment starts at the center and ends on the circle, it is a radius, and half of a diameter.

🔍 Related terms

radius of a circle, secant line, tangent line