Concept 10.1
What Makes a Line a Tangent
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
A line that intersects a circle in exactly one point is called a tangent to the circle; the common point is the point of contact. A line meeting a circle in two points is a secant.
The intuition
A line and a circle can share two points, one point, or none. The tangent is the borderline case: slide a secant away until its two meeting points merge into one.
So 'tangent' is a statement about how many points are shared, not about how close the line looks. A line that misses the circle by a hair is not a tangent.
The attention
Look at how many points the line shares with the circle.
secant: two common points, tangent: exactly one, no common point
Look hereNot here
- Look here
- Exactly one common point. A tangent shares exactly one point with the circle: the point of contact.
- Not here
- No common point. A line that only looks as if it touches may share no point at all. Count, don't eyeball.
- What it teaches
- Turn 'looks like' into something you can count.