medium difficulty5 min

Identifying tangent and secant situations

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

In one line: One touch, tangent. Two cuts, secant.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

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

Worked example

1If line l touches the circle at only A, l is a tangent.
2If line m cuts the circle at B and C, m is a secant.

Method you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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.

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.

Don't mix this up

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

Exam tip

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

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

1
Enough for 1 mark
A tangent touches a circle at one point, while a secant cuts the circle at two points.
2
Add for 2 marks
Example: A line cutting a circle at A and B is a secant. A line touching only at C is a tangent.
3
Add for 3 marks
If a line just touches once, it is a tangent.

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