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Class 9 Maths: I'm Up and Down, and Round and Round (Circles), 8 practice questions with answers
These are 8 practice questions on Chapter 5, I'm Up and Down, and Round and Round, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). The chapter is about circles. Each question has a worked answer and the textbook page it comes from. They cover a chord's distance from the centre, the length of a chord, the radius from a chord, equal chords, which of two chords is nearer the centre, the angle an arc subtends, the angle in a semicircle and the opposite angles of a cyclic 4-gon. Try each one on paper before you open the answer. In Class 10 the circle ideas continue with tangents in the Class 10 Circles questions.
These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 5, printed pages 92 to 117):
- A chord joins two points of a circle, and the angle it subtends at the centre is the angle between the two radii to its ends (page 93). There is exactly one circle through three points that are not on a line (Theorem 1, page 96).
- Equal chords subtend equal angles at the centre (Theorem 2, page 99), and the converse holds (Theorem 3, page 100).
- The perpendicular from the centre to a chord bisects the chord (Theorem 5, page 102). So the radius r, the distance d from the centre and half the chord make a right triangle, and the chord is 2√(r² − d²) (Exercise Set 5.5, page 105).
- Equal chords are equally far from the centre (Theorem 6, page 103); the longer of two chords is nearer the centre, and a diameter is the greatest chord (Theorem 8 and the comment after it, page 105).
- The angle an arc subtends at the centre is double the angle it subtends at any point on the circle outside the arc (Theorem 9, page 108). So the angle subtended by a diameter at any point on the circle is 90° (Corollary, page 110).
- The opposite angles of a cyclic quadrilateral add up to 180° (Theorem 11, page 112).
Chords and the centre
Question 1. A circle has radius 58 cm. A chord of length 84 cm is drawn in it. How far is the chord from the centre?
Answer: 40 cm. The perpendicular from the centre bisects the chord, so half the chord is 42 cm. Radius, distance and half-chord make a right triangle: distance = √(58² − 42²) = √(3364 − 1764) = √1600 = 40 cm. (Theorem 5, page 102; Baudhāyana–Pythagoras theorem, as the book uses it on page 105.)
Question 2. A chord is 51 cm from the centre of a circle of radius 149 cm. How long is the chord?
Answer: 280 cm. Half the chord = √(149² − 51²) = √(22201 − 2601) = √19600 = 140 cm, so the chord is 2 × 140 = 280 cm. (The chord is 2√(r² − d²), Exercise Set 5.5, page 105; Theorem 5, page 102.)
Question 3. A chord of length 154 cm is 36 cm from the centre of a circle. What is the radius?
Answer: 85 cm. Half the chord is 77 cm, and the radius is the hypotenuse: √(77² + 36²) = √(5929 + 1296) = √7225 = 85 cm. (Theorem 5, page 102.)
Question 4. In one circle, chord PQ is 27 cm long and chord RS is 31 cm long. Which chord is nearer the centre?
Answer: RS, the 31 cm chord. Of two chords of a circle, the longer one is nearer the centre. (Theorem 8, page 105.)
Question 5. AB and CD are equal chords of a circle with centre O, and ∠AOB = 52°. What is ∠COD?
Answer: 52°. Equal chords subtend equal angles at the centre, so ∠COD = ∠AOB = 52°. (Theorem 2, page 99.)
Angles in a circle
Question 6. An arc subtends an angle of 124° at the centre of a circle. What angle does it subtend at a point on the circle outside the arc?
Answer: 62°. The angle at the centre is double the angle at the circle, so the angle at the point is 124° ÷ 2 = 62°. (Theorem 9, page 108.)
Question 7. AB is a diameter of a circle and C is another point on the circle. If ∠CAB = 34°, find ∠ABC.
Answer: 56°. The angle subtended by a diameter at a point on the circle is 90°, so ∠ACB = 90°. The angles of triangle ABC add up to 180°: ∠ABC = 180° − 90° − 34° = 56°. (Corollary, page 110.)
Question 8. ABCD is a cyclic quadrilateral (all four vertices lie on one circle) and ∠A = 59°. Find ∠C, the angle opposite A.
Answer: 121°. Opposite angles of a cyclic quadrilateral add up to 180°, so ∠C = 180° − 59° = 121°. (Theorem 11, page 112.)
Practise more, and check your marks
- There is no practice set for this chapter yet. Free practice on other Class 9 chapters, marked instantly in your browser: Class 9 practice.
- Printable Class 9 worksheets with answer keys, in English, Hindi and Marathi: Class 9 worksheets.
- The chapter right after this one, with circles again (circumference and area): Class 9 Measuring Space, 8 practice questions.
- Another Class 9 Maths guide in this style: Class 9 Introduction to Linear Polynomials.
- The first chapter of this Class 9 book: Ganita Manjari Class 9 Chapter 1, coordinates, explained.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 91.
- NCERT, Ganita Manjari: Textbook of Mathematics for Grade 9, Part I (First Edition, April 2026), Chapter 5 "I'm Up and Down, and Round and Round", printed pages 92-117 (chords and subtended angles, page 93; Theorem 1, page 96; Theorem 2, page 99; Theorem 3, page 100; Theorem 5, page 102; Theorem 6, page 103; Theorem 8, the greatest chord and the chord length 2√(r² − d²), page 105; Theorem 9, page 108; the angle subtended by a diameter, page 110; Theorem 11, page 112): ncert.nic.in/textbook/pdf/iemh105.pdf
- NCERT, Ganita Manjari: Textbook of Mathematics for Grade 9, Part I, front matter and contents (chapter titles and starting pages): ncert.nic.in/textbook/pdf/iemh1ps.pdf
The theorems are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.