Meaning & use
point of tangency
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Meanings
nouncountabletechnicalmathematics
The single point where a straight line touches a curve or a circle without crossing it.
Grammar: Countable; usually used with 'the' in geometry: the point of tangency.
Patterns
- the point of tangency between something and something
- the point of tangency of a line and a curve
In the diagram, the line touches the circle at exactly one point of tangency.
Find the point of tangency between the straight line and the parabola.
The radius drawn to the point of tangency is perpendicular to the tangent line.
nouncountablefigurative
A moment or issue where two things briefly meet or connect without fully merging.
Grammar: Countable and often figurative; use 'a' or 'the' before it.
Patterns
- a point of tangency between something and something
The two research fields share only a small point of tangency.
Their interests met at a single point of tangency: the problem of clean water.
Word forms
| plural | points of tangency |
|---|
Common combinations
- the point of tangency
- The teacher marked the point of tangency on the board.
- find the point of tangency
- Students had to find the point of tangency using algebra.
- at the point of tangency
- At the point of tangency, the slope of the curve equals the slope of the line.
- point of tangency between
- There is a point of tangency between the two ideas.
Synonyms and how they differ
- point of contact
- Wider and more general; it can mean any place where two things touch, not only in geometry.
Word family
- tangent noun
- A straight line that touches a curve at one point.
- tangent adjective
- Touching a curve at one point, as in a tangent line.
- tangential adjective
- Relating to a tangent, or only slightly connected to a main subject.
Commonly confused: point of tangency or point of intersection?
point of tangency vs point of intersection
A point of intersection is where two lines or curves cross each other; a point of tangency is where they just touch without crossing.
Practice
A line touches a circle at exactly one point. What is that point called?
Choose one answer.
'Point of tangency' is the correct term for the single point where a line touches a curve or circle. 'Point of intersection' is wrong because intersecting lines cross at two points on a circle, not just touch at one.
Make it your own
Write a sentence using “point of tangency”, then check it and compare it with the examples above.