Circles Exercise 5.3 Class 9 Maths NCERT Solutions

The Circles Exercise 5.3 set uses the rule that a perpendicular from the centre bisects a chord. These NCERT Solutions Class 9 Maths Chapter 5 Circles Exercise 5.3 answers turn that rule into a right triangle. You then use the Pythagoras step to find chord distances and lengths.

• Questions solved: all 3 problems of Exercise 5.3
• Main skill: the perpendicular from the centre bisecting a chord
• Chapter link: it sets up the chord length formula in Exercise 5.5

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 5.3 Cover?

Exercise 5.3 builds on one theorem. When you drop a perpendicular from the centre to a chord, it cuts the chord in half. This makes a right triangle with the radius, the half-chord, and the distance from the centre. The set asks you to explain the converse, work with an inscribed isosceles triangle, and find a distance between two parallel chords. Every answer uses the same right triangle. So learning it once helps you solve all three. Keep the radius as the hypotenuse and the half-chord as one leg.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Circles Exercise 5.3 Question Breakdown

The set has three questions.

Sample Solved Question from Exercise 5.3

Here is Question 3, solved in short steps.

Question: Two parallel chords of lengths 6 cm and 8 cm lie on opposite sides of the centre of a circle of radius 5 cm. Find the distance between their midpoints.

Step 1. For the 6 cm chord, half is 3 cm. Its distance is d₁=√5²-3²=√16=4 cm.

Step 2. For the 8 cm chord, half is 4 cm. Its distance is d₂=√5²-4²=√9=3 cm.

Step 3. The chords lie on opposite sides of the centre, so the distances add.

Final answer. The gap is d₁+d₂=4+3=7 cm.

How to Use These Circles Exercise 5.3 Solutions

Collegedunia draws the right triangle for each chord, so you can see where the numbers come from. Use the answers step by step.

• Halve the chord first, then place it as one leg of the right triangle.
• Use the radius as the hypotenuse, never as a leg.
• Check whether the chords are on the same or opposite sides before you add or subtract.

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.