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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

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

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

The number of tangents from a point depends on whether the point lies inside, on, or outside the circle. Outside point: 2 tangents; point on circle: 1 tangent; inside point: 0 tangents. From an external point P, tangents PA and PB can be drawn to the circle.

3-mark answer

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. Outside point: 2 tangents; point on circle: 1 tangent; inside point: 0 tangents. If point P lies outside a circle, two tangents PA and PB can be drawn. If point Q lies on the circle, only one tangent is possible. This is often asked as a direct short answer or as part of a diagram-based reasoning question. A common wrong answer is to say two tangents are always possible. That fails for points on or inside the circle.
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