Circles Exercise 5.4 Class 9 Maths NCERT Solutions

The Circles Exercise 5.4 set proves that equal chords stay the same distance from the centre. These NCERT Solutions Class 9 Maths Chapter 5 Circles Exercise 5.4 answers build the distance formula from a right triangle. You then see clearly why chords of equal length are equidistant.

• Questions solved: all 3 problems of Exercise 5.4
• Main skill: equal chords lie at equal distance from the centre
• Chapter link: it pairs with Exercise 5.3 to complete the chord theorems

These Collegedunia solutions are written by subject teachers, matched to the current 2026-27 Ganita Manjari book, and checked line by line. Each answer stays in plain language, with the reason behind every line spelled out, so a Class 9 student can follow it on the first read.

What Does Class 9 Maths Chapter 5 Circles Exercise 5.4 Cover?

Exercise 5.4 studies equal chords. It shows that the distance of a chord from the centre depends only on the radius and the chord length. So two chords of the same length must be the same distance away. The proof uses the same right triangle as before, with the radius, the half-chord, and the distance. The set then applies this to a labelled figure. Once the formula is clear, the equal-chord result follows in one line. The same idea returns often in later circle problems.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Circles Exercise 5.4 Question Breakdown

The set has three questions.

Sample Solved Question from Exercise 5.4

Here is Question 1, written as a short proof.

Question: Use the Pythagoras rule to show why chords of the same length are at the same distance from the centre.

Step 1. Take a chord AB of length in a circle of radius r. Drop a perpendicular from the centre to its midpoint M, so AM=2.

Step 2. In the right triangle, r²=d²+(2)², where d is the distance from the centre.

Step 3. Solve for the distance: d=√r²-(2)².

Final answer. This d depends only on r and . Equal chords share the same , so they give the same d and are equidistant.

How to Use These Circles Exercise 5.4 Solutions

Collegedunia derives the formula first, then reads the result straight from it. Use the answers in that order.

• Set up the right triangle with the radius as the hypotenuse.
• Write the distance as a formula in r and before you plug in numbers.
• For a spot-check, try r=5 and =6: the distance comes out as 4.

Work through the questions in order the first time, then use these solutions only to check your own steps. Redoing a question after you read the answer fixes the method far better than reading alone. A short daily set of these problems builds a firm base for the Class 9 annual exam and the circle theorems you meet in the Class 10 syllabus.

More Class 9 Maths Circles Solutions

Open the full chapter or any other exercise of Class 9 Maths Chapter 5 Circles from the table below.