Touching, not crossing
Show on a big screenA drawn wheel meets a flat road at one point.
- One circle.
- A line that misses — 0 shared points.
- A line that touches once — a tangent.
- A line that cuts through — 2 shared points — a secant.
One point, and no crossing
A straight line can meet a circle three ways. It can miss the circle. It can cut through it. It can touch it at exactly one point.
A tangent touches a circle at one point. It does not go inside the circle. That one shared point is the point of contact. In the drawing, the wheel and the road share just that point.
A line that cuts through the circle meets it at two points. The book calls this a secant. A chord is the piece of a secant inside the circle.
| The line | Shared points | Name |
|---|---|---|
| Misses the circle entirely | none | — |
| Cuts through the inside | two | secant |
| Touches the edge | exactly one | tangent |
The word "tangent" comes from a Latin word that means "touching".
Measure the shortest distance from the centre to the line. Then compare it with the radius. More than the radius: the line misses. Equal to the radius: it touches. Less than the radius: it cuts.
Compare the distance with the radius. Tap how the line meets the circle.
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Try the lab to finish this lesson.