# How many tangents can a circle have?

Last updated date: 18th Mar 2023

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Answer

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Hint:- Go with definitions of tangents and circle.

As we know that for any conic,

Locus is the set of all points whose coordinates satisfy a given equation or condition.

And as we know that,

Circle is the locus of points equidistant from a given point, which is the centre of the circle.

And, tangent is the line which intersects a circle at one point only.

The circle has infinite points. So, there will be infinite tangents that can be drawn

on these points which touches at only one point.

Hence, a circle can have infinite tangents.

Note:- Whenever we came up with this type of questions, then remember that tangents intersect

the circle at one point and chords cut the circle at two points. So, there can be infinite number of

chords and tangents that can be drawn on a circle. And remember that diameter is also a chord to

the circle with length as 2r.

As we know that for any conic,

Locus is the set of all points whose coordinates satisfy a given equation or condition.

And as we know that,

Circle is the locus of points equidistant from a given point, which is the centre of the circle.

And, tangent is the line which intersects a circle at one point only.

The circle has infinite points. So, there will be infinite tangents that can be drawn

on these points which touches at only one point.

Hence, a circle can have infinite tangents.

Note:- Whenever we came up with this type of questions, then remember that tangents intersect

the circle at one point and chords cut the circle at two points. So, there can be infinite number of

chords and tangents that can be drawn on a circle. And remember that diameter is also a chord to

the circle with length as 2r.

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