Circles End of Chapter Class 9 Maths NCERT Solutions

The Circles End-of-Chapter set gathers 26 mixed problems on every idea in the chapter. These NCERT Solutions Class 9 Maths Chapter 5 Circles cover chord lengths, central angles, cyclic quadrilaterals, and short proofs. It is the best set for full revision before your Class 9 annual exam.

• Questions solved: all 26 End-of-Chapter problems
• Main skills: chords, arcs, cyclic quadrilaterals, and proofs
• Chapter link: it revises Exercises 5.1 to 5.6 in one place

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 End-of-Chapter Set Cover?

The End-of-Chapter set is a full mix. Some questions ask for chord lengths and distances from the centre. Others use central angles, arcs, and the angle in a semicircle. Several deal with cyclic quadrilaterals and their angle sums. A few are short proofs, and some cover inscribed shapes like a rectangle or a regular hexagon. Solving them checks the whole chapter at once.

Video Walkthrough

Source: PW Class 9 - NEEV on YouTube

Circles End of Chapter Question Breakdown

The 26 questions group into a few clear themes.

• Chord length and distance: find a chord or its distance from the centre (Q1, Q3, Q4, Q9, Q13, Q18).
• Central angles and arcs: use central angles and the angle in a semicircle (Q2, Q6).
• Cyclic quadrilaterals: opposite angles, exterior angles, and area (Q7, Q8, Q10, Q11, Q20, Q21).
• Short proofs: the perpendicular bisector through the centre, and the longest chord (Q5, Q22, Q23).
• Inscribed shapes: a rectangle in a circle and a regular hexagon (Q14, Q15, Q19).
• Intersecting and congruent chords: chords that meet or are equal (Q12, Q17, Q25).

Sample Solved Question from End of Chapter

Here is Question 3, solved in short steps.

Question: The diameter of a circle is 26 cm. A chord of length 24 cm is drawn. Find the distance from the centre to the chord.

Step 1. The diameter is 26 cm, so the radius is r=262=13 cm.

Step 2. The perpendicular from the centre bisects the chord, so half of it is 242=12 cm.

Step 3. Use the right triangle: d=√13²-12²=√169-144=√25.

Final answer. The distance is d=5 cm, matching the 5-12-13 right triangle.

How to Use These Circles End of Chapter Solutions

Collegedunia sorts these 26 answers by topic, so you can revise one idea at a time. Use the set for final practice.

• Sort the questions by theme and solve one group at a time.
• For any chord problem, draw the radius and the perpendicular first.
• Use the opposite-angle rule for every cyclic quadrilateral question.

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.