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Identifying tangent and secant situations

A tangent touches a circle at one point, while a secant cuts the circle at two points.

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Student-friendly explanation

Many exam diagrams mix tangents, secants, and chords. You must read the figure carefully. If a line just touches once, it is a tangent. If it passes through and meets the circle at two points, it is a secant. If it joins two points on the circle, it is a chord.

How to write this in exams

  1. 1

    Start with the exact idea

    A tangent touches a circle at one point, while a secant cuts the circle at two points.

  2. 2

    Then show how to use it

    1. Observe the line and the circle. 2. Count the common points. 3. If only one point is common, write tangent. 4. If two points are common, write secant.

  3. 3

    Add one concrete example

    A line cutting a circle at A and B is a secant. A line touching only at C is a tangent.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to call every touching line a chord or every cutting line a tangent. The point count decides the answer.

Definition

A tangent touches a circle at one point, while a secant cuts the circle at two points.

Example

A line cutting a circle at A and B is a secant. A line touching only at C is a tangent.

Rule to remember

One common point means tangent; two common points mean secant.

Memory hook

One touch, tangent. Two cuts, secant.

Examples and method

Worked example

If line l touches the circle at only A, l is a tangent. If line m cuts the circle at B and C, m is a secant.

Method to apply

1. Observe the line and the circle. 2. Count the common points. 3. If only one point is common, write tangent. 4. If two points are common, write secant.

Diagram support

Use small labels A, B, and C on the circle boundary to show where the line meets the circle.

How CBSE asks it

This is commonly asked through diagrams where students must identify each line correctly.

Avoid common mistakes

Common confusion

Students often confuse a secant with a chord because both involve two points on the circle.

Common wrong answer

A common wrong answer is to call every touching line a chord or every cutting line a tangent. The point count decides the answer.

Exam tip

Count intersections with the circle before naming the line. One point means tangent, two points mean secant.

Quick check

How do you distinguish a tangent from a secant in a circle diagram?

A tangent touches the circle at exactly one point, while a secant cuts the circle at two points. Counting the common points gives the correct name.

Answer writing and exam use

1-mark answer

A tangent touches a circle at one point, while a secant cuts the circle at two points.

2-mark answer

A tangent touches a circle at one point, while a secant cuts the circle at two points. One common point means tangent; two common points mean secant. A line cutting a circle at A and B is a secant. A line touching only at C is a tangent.

3-mark answer

Many exam diagrams mix tangents, secants, and chords. You must read the figure carefully. If a line just touches once, it is a tangent. If it passes through and meets the circle at two points, it is a secant. If it joins two points on the circle, it is a chord. One common point means tangent; two common points mean secant. If line l touches the circle at only A, l is a tangent. If line m cuts the circle at B and C, m is a secant. This is commonly asked through diagrams where students must identify each line correctly. A common wrong answer is to call every touching line a chord or every cutting line a tangent. The point count decides the answer.
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