medium difficulty5 min

Number of tangents from a point

The number of tangents from a point depends on whether the point lies inside, on, or outside the circle.

In one line: Outside: two, on: one, inside: none.

Practice This Concept

Understand it

From a point outside a circle, two tangents can be drawn.
From a point on the circle, only one tangent can be drawn.
From a point inside the circle, no tangent can be drawn.
This result is very useful in figure-based questions.

Example

From an external point P, tangents PA and PB can be drawn to the circle.

Formula and rule

Outside point: 2 tangents; point on circle: 1 tangent; inside point: 0 tangents.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1If point P lies outside a circle, two tangents PA and PB can be drawn.
2If point Q lies on the circle, only one tangent is possible.

Method you can reuse

1Locate the point.
2Check whether it is outside, on, or inside the circle.
3Use the correct count of tangents.
4State the answer clearly.

Sketch it in your answer

Show three small sketches: one point outside, one on the circle, and one inside the circle.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

How many tangents can be drawn from a point inside a circle?

Think first, then show answer

No tangent can be drawn from a point inside a circle. A tangent touches the circle only at one point, and an interior point cannot touch the circle from outside.

Common wrong answer

A common wrong answer is to say two tangents are always possible. That fails for points on or inside the circle.

Don't mix this up

Students often say two tangents can be drawn from any point. That is not true for points inside the circle.

Exam tip

First check the position of the point relative to the circle. That decides the number of tangents immediately.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

This is often asked as a direct short answer or as part of a diagram-based reasoning question.

1
Enough for 1 mark
The number of tangents from a point depends on whether the point lies inside, on, or outside the circle.
2
Add for 2 marks
Example: From an external point P, tangents PA and PB can be drawn to the circle.

MCQ Quiz

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