Circles Exercise 5.1 Class 9 Maths NCERT Solutions

The Circles Exercise 5.1 set teaches you to draw the circumcircle of a triangle. These NCERT Solutions Class 9 Maths Chapter 5 Circles Exercise 5.1 answers show each construction step with a labelled figure. You learn to find the circumcentre and the smallest circle through two given points.

• Questions solved: all 4 problems of Exercise 5.1
• Main skills: drawing circumcircles and locating the circumcentre
• Chapter link: it opens the circle work used in every later exercise

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 5.1 Cover?

Exercise 5.1 is about construction. You draw a triangle first, then build the one circle that passes through all three corners. That circle is the circumcircle, and its centre is the circumcentre. The set also asks for the smallest circle through two given points. Each answer uses only a ruler and compass, so you can copy the steps in your own notebook.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Circles Exercise 5.1 Question Breakdown

The set has four questions. The table shows what each one asks.

Sample Solved Question from Exercise 5.1

Here is Question 4, solved in short steps.

Question: What is the least possible radius of a circle through two points A and B?

Step 1. If a circle passes through A and B, then AB is a chord. A chord is never longer than the diameter, so AB ≤ 2R.

Step 2. Divide both sides by 2. This gives R ≥ AB2, so no circle through the two points can be smaller.

Step 3. The radius is smallest when AB is a diameter. Then the centre sits at the midpoint of AB.

Final answer. The least possible radius is AB2, half the distance between the points.

How to Use These Circles Exercise 5.1 Solutions

Collegedunia keeps each construction split into clear compass and ruler steps, so you can build the figure yourself. Use the answers this way.

• Read the given sides and angles before you start the drawing.
• Keep the compass width fixed while you strike each pair of arcs.
• Check the circumcentre by measuring: all three corners must be the same distance away.

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.