Circle Vocabulary: Center, Radius, Chord, Secant, Tangent
Every circle theorem you'll learn this year is written in the same six words: center, radius, diameter, chord, secant, tangent. If you can name each part instantly, the theorems read like plain English. If you can't, every problem starts with a translation step you don't need.
The good news is that each word is a short, checkable definition about where a segment or line touches the circle. Learn the definitions once, and identifying any part of a circle takes two questions: where are the endpoints, and how many times does it meet the circle?
Segments in a circle
A radius runs from the center to a point on the circle. Every radius of a circle has the same length, and that length is what we mean by 'the radius' as a number.
A chord is a segment with both endpoints on the circle. It doesn't have to pass through the center — most chords miss it.
A diameter is the special chord that does pass through the center. It's the longest chord a circle has, and its length is twice the radius: . The diagram below shows all three.
Lines that meet a circle
A secant is a line that crosses the circle at two points. Think of it as a chord that keeps going in both directions.
A tangent is a line that touches the circle at exactly one point, called the point of tangency. It grazes the circle without crossing into it, and it's always perpendicular to the radius drawn to that point. In the figure below, the secant cuts through, while the tangent meets the circle once and makes a right angle with the radius.
How to tell them apart fast
Ask two questions. First: is it a segment or a line? Radii, chords, and diameters are segments; secants and tangents are lines. Second: how does it meet the circle? Both endpoints on the circle means chord (through the center means diameter). One endpoint at the center means radius. Crosses at two points means secant; touches at one point means tangent.
Worked examples
Example 1: naming a segment
Segment has both endpoints on circle and does not pass through . What is it?
Answer: is a chord.
Example 2: radius from a diameter
A circle has a diameter of cm. Find its radius.
Answer: cm
Example 3: secant or tangent?
Line meets a circle at exactly one point, and line meets the same circle at two points. Name each line.
Answer: Line is a tangent; line is a secant.
Try one yourself
Common questions
Is a diameter a chord?
Yes. A chord only needs both endpoints on the circle, and a diameter has that — it just also passes through the center. Every diameter is a chord, but most chords are not diameters.
Is a radius a chord?
No. A radius has one endpoint at the center, which is not on the circle. A chord needs both endpoints on the circle itself.
What's the difference between a chord and a secant?
A chord is a segment — it stops at the circle. A secant is a full line that passes through those same two points and keeps going. Every secant contains a chord.
Can a tangent line cross the circle if you extend it?
No. A tangent touches the circle at exactly one point no matter how far you extend it. If extending a line would give a second intersection point, it was a secant all along.
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