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CBSE Class 9 Mathematics Chapter 5 I'm Up and Down, and Round and Round Worksheet with Answers

Welcome to the comprehensive worksheet for CBSE Class 9 Mathematics Chapter 5 'I'm Up and Down, and Round and Round'. This chapter explores the elegant geometry of circles — from chords and arcs to angles and cyclic quadrilaterals. This worksheet is designed to test your conceptual understanding and problem-solving skills across multiple question formats: MCQs, fill-in-the-blanks, true/false, short answers, long answers, and a case study. Print this page, set aside 90 minutes, and challenge yourself. All answers with brief explanations are provided at the end.

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Key takeaways

✓A circle is defined as the locus of points equidistant from a fixed centre; this property underpins all circle theorems.
✓The perpendicular from the centre to any chord bisects the chord; equal chords are equidistant from the centre.
✓An arc subtends an angle at the centre that is twice the angle subtended at any point on the remaining part of the circle.
✓Any angle inscribed in a semicircle is a right angle — a direct corollary of the inscribed angle theorem.
✓In a cyclic quadrilateral, opposite angles sum to 180 degrees, providing a definitive test for concyclicity.
✓Equal chords of a circle subtend equal angles at the centre, linking geometric length and angular measure.
✓This worksheet includes a case-study question and HOTS problems to mirror the latest CBSE exam pattern for Class 9.

Quick Chapter Recap: Circles, Chords, Angles, and Cyclic Quadrilaterals

Chapter 5 'I'm Up and Down, and Round and Round' is a deep dive into the properties of circles. A circle is the set of all points in a plane at a fixed distance (radius) from a fixed point (centre). Every radius of the same circle is equal. A chord is a line segment joining any two points on the circle; the longest chord is the diameter, which passes through the centre and equals twice the radius. A fundamental property states that the perpendicular from the centre to a chord bisects that chord. Equal chords are equidistant from the centre, and conversely, chords equidistant from the centre are equal in length. The chapter then explores arcs and the angles they subtend: an arc subtends an angle at the centre that is double the angle it subtends at any other point on the circle. This leads to the beautiful result that any angle in a semicircle is a right angle. Finally, cyclic quadrilaterals (quadrilaterals whose vertices all lie on a circle) have the property that opposite angles sum to 180 degrees. Mastering these concepts requires both memorising key theorems and practicing their application in diverse problem contexts.

Circle: locus of points equidistant from a centre
Perpendicular from centre bisects any chord
Equal chords subtend equal angles at centre and are equidistant from centre
Angle at centre = 2 × angle at circumference (same arc)
Angle in semicircle = 90 degrees
Cyclic quadrilateral: opposite angles sum to 180 degrees

Difficulty Level and Suggested Time

This worksheet has been carefully calibrated to match CBSE Class 9 examination standards. The difficulty level is Medium to High, with a progressive increase in complexity from Section A (MCQs) to Section E (HOTS long-answer questions). The worksheet includes 6 multiple-choice questions, 5 fill-in-the-blanks, 5 true/false statements, 5 short-answer questions (2-3 marks each), 3 long-answer/HOTS questions (4-5 marks each), and 1 case-study question with sub-parts. Students should allocate approximately 90 minutes to complete the entire worksheet under exam-like conditions. However, if you are using this for topic-wise practice, you may attempt individual sections in shorter sittings. We recommend attempting all questions on your own first, then checking the detailed answer key provided at the end. Time yourself to build exam temperament and speed. For personalized doubt-clearing and step-by-step guided solving, consider CBSETUTOR.ai — your 24x7 AI tutor that explains every step, accepts photo uploads of your work, and offers unlimited practice at a flat fee of just ₹999 per month for all classes 6 to 12, with a 3-day free trial.

Difficulty: Medium to High
Total time: 90 minutes (full worksheet)
Section-wise practice: 10-15 minutes per section
Self-assess first, then review answers
Use timer to simulate exam pressure

Section A: Multiple Choice Questions (1 mark each)

Multiple-choice questions test your ability to quickly recall definitions, properties, and apply basic reasoning. Read each question carefully, eliminate obviously wrong options, and choose the best answer. Each MCQ carries 1 mark. Negative marking is not applied in this worksheet, but in actual CBSE exams, guess wisely. These six questions cover the breadth of Chapter 5: definitions of circle elements, chord properties, angle theorems, and cyclic quadrilaterals. Practice identifying the correct property or theorem that applies to each scenario. If you find yourself unsure, revisit the quick recap above or your NCERT Class 9 Mathematics textbook before attempting. Remember, MCQs often test conceptual clarity rather than lengthy calculations, so focus on understanding the 'why' behind each theorem. For example, knowing that the perpendicular from the centre bisects a chord is not enough — you should also know the converse and be able to apply it in a diagram-based question. Strong performance in this section builds confidence for the tougher sections ahead.

Section B: Fill in the Blanks (1 mark each)

Fill-in-the-blank questions require precise recall of terminology, formulas, and properties. Write your answers neatly in the blanks provided. Each correct answer earns 1 mark. These questions are designed to reinforce your memory of key facts from Chapter 5. For example, you should be able to state without hesitation that all points on a circle are equidistant from the centre, or that the sum of opposite angles in a cyclic quadrilateral is 180 degrees. Fill-in-the-blanks often appear straightforward but can be tricky if you confuse similar-sounding terms (like 'radius' and 'diameter') or misremember a property. Use this section to self-diagnose gaps in your foundational knowledge. If you struggle with any blank, mark it, complete the rest, and return to review your NCERT notes. Strong performance here indicates solid conceptual grounding. Weak performance signals the need for focused revision before tackling application-based short and long answers. Keep your answers concise and mathematically accurate. Avoid vague or incomplete statements.

Section C: True or False (1 mark each)

For each statement below, write 'True' if the statement is always correct, or 'False' if it is incorrect or only sometimes correct. True/False questions test your ability to judge the validity of geometric propositions. A single counterexample is enough to prove a statement false. For instance, 'All chords of a circle are equal' is false because only the diameter is the longest chord; other chords vary in length depending on their distance from the centre. Conversely, 'The perpendicular from the centre bisects any chord' is true by the fundamental chord-bisector theorem. Pay close attention to absolute words like 'always', 'never', 'all', and 'every' — they often signal that you should check edge cases. If a statement says 'A cyclic quadrilateral always has all sides equal', think of a cyclic trapezium: opposite angles sum to 180 degrees, but sides need not be equal, so the statement is false. This section sharpens your logical reasoning and helps you distinguish between necessary conditions, sufficient conditions, and coincidental properties. Each question carries 1 mark, so budget about one minute per statement.

Section D: Short Answer Questions (2-3 marks each)

Short-answer questions require you to apply theorems, perform calculations, and provide brief justifications. Each question in this section carries 2 to 3 marks. Marks are awarded not just for the final answer but also for correct reasoning and clear presentation of steps. For example, if asked to prove that equal chords subtend equal angles at the centre, you must state the given information, draw and label a diagram, cite the congruence criterion (SSS or SAS), and conclude logically. Avoid skipping steps or writing 'obvious' without proof — examiners reward methodical work. Manage your time: allocate about 4-5 minutes per 2-mark question and 6-7 minutes per 3-mark question. Use diagrams wherever helpful; a well-labelled figure often earns you a mark even if your calculation has a minor error. Practice writing concise but complete answers: state the property or theorem you are using, show the calculation or logical deduction, and box or underline your final answer. These questions mirror the style and difficulty of CBSE Class 9 board and school exams, so regular practice here builds exam confidence and scoring ability.

Section E: Long Answer and HOTS Questions (4-5 marks each)

Long-answer and Higher Order Thinking Skills (HOTS) questions demand multi-step reasoning, integration of multiple theorems, and often creative problem-solving. Each question here carries 4 to 5 marks. Examiners look for clarity of thought, logical flow, accurate diagrams, correct application of theorems, and neat presentation. For instance, a HOTS question might ask you to prove a property of cyclic quadrilaterals using the angle-subtended theorem, or to find an unknown length by combining the perpendicular-bisector theorem with Pythagoras. Allocate 8-10 minutes per question. Start by reading the question twice and identifying what is given and what is to be proved or found. Draw a large, clear, and well-labelled diagram. Write 'Given', 'To Prove/Find', and 'Proof/Solution' headings to organize your answer. Cite theorems by name or number when you use them. Show all algebraic steps; do not jump to the answer. If the question has multiple parts, answer them in order and ensure each part logically supports the next. HOTS questions often test your ability to synthesize knowledge from different sections of the chapter, so expect to use chord properties, angle theorems, and cyclic quadrilateral properties all in one solution.

Section F: Case-Study Based Question (4 marks)

Case-study questions present a real-world or application scenario and ask you to apply your understanding of circle properties to solve sub-questions. This format has been introduced in recent CBSE exams to test conceptual application and analytical skills. Read the case study carefully, underline or highlight key numerical data and geometric facts, and visualize or sketch the scenario. The case study below describes a circular garden with pathways (chords) and a fountain (centre). You are asked to find lengths, angles, and verify properties using the theorems from Chapter 5. Each sub-question typically carries 1 mark. Answer all parts in sequence, and show brief working where required. Marks are awarded for correct reasoning and accurate calculations. Even if you are unsure about one sub-question, attempt the others — they are often independent. Case-study questions reward students who can translate a verbal or pictorial scenario into geometric diagrams and equations. They also test your ability to identify which theorem applies in a given context. Practice such questions regularly to build confidence for the board exam pattern.

Answer Key with Explanations

Below is the complete answer key for all sections of this worksheet. Each answer includes a brief explanation or working to help you understand the reasoning. Use this key only after you have attempted all questions on your own. Self-assessment is a powerful learning tool: compare your answers, identify mistakes, and revisit the relevant theorem or concept in your NCERT textbook or notes. If you got an answer wrong, do not just copy the correct answer — understand why your approach was incorrect and redo the question from scratch. For calculation errors, check each arithmetic step. For conceptual errors, re-read the theorem and work through a similar example. If you are stuck on any explanation in this key, consider reaching out to CBSETUTOR.ai, where you can upload a photo of your working and get instant, personalized feedback from an AI tutor available 24x7. The platform costs just ₹999 per month for all subjects and classes 6-12, with a 3-day free trial. Regular practice with worksheets like this one, combined with active self-correction using answer keys, is the best strategy to master CBSE Class 9 Mathematics Chapter 5 and score high in exams.

Section A (MCQs): 1.(b) 2.(a) 3.(c) 4.(c) 5.(b) 6.(c)
Section B (Fill-in-the-Blanks): 1. equidistant 2. bisects 3. equidistant 4. twice 5. 180
Section C (True/False): 1. True 2. True 3. False (it is 90°) 4. True 5. False (sum must be exactly 180°)
Sections D, E, F: Detailed solutions below

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Worksheets like this one are excellent for practice, but what happens when you are stuck on a tricky proof or cannot spot the hidden triangle in a diagram? That is where CBSETUTOR.ai comes in. CBSETUTOR.ai is your personal 24×7 AI Mathematics tutor, designed specifically for CBSE students in classes 6 to 12. Simply snap a photo of any question from this worksheet (or your textbook, or any other source), upload it to the platform, and receive step-by-step solutions with clear explanations in seconds. The AI tutor does not just give you the answer — it walks you through the reasoning, highlights which theorem applies, and even suggests similar practice questions to strengthen your understanding. Whether you are revising late at night before an exam or need help with homework on a Sunday afternoon, CBSETUTOR.ai is always available. The best part? One flat fee of just ₹999 per month covers all subjects and all classes from 6 to 12, with no hidden charges. You also get a risk-free 3-day trial to explore the platform and see how it transforms your learning. Thousands of CBSE students across India are already using CBSETUTOR.ai to clarify doubts, practice smarter, and score higher. Join them today and make circle geometry — and every other CBSE Maths topic — easy and enjoyable.

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Frequently asked questions

What topics from Chapter 5 are covered in this worksheet?+

This worksheet covers all major topics: definition of a circle, radius and diameter, properties of chords, perpendicular from centre to chord, equal chords and equal angles, angle subtended by an arc at centre and circumference, angle in a semicircle, and cyclic quadrilaterals with the opposite-angle-sum property.

How much time should I take to complete this worksheet?+

Allocate approximately 90 minutes to complete the entire worksheet under exam conditions. You may split it into sections if practicing topic-wise: 10 minutes for MCQs, 5 minutes for fill-in-the-blanks, 5 minutes for true/false, 25 minutes for short answers, 30 minutes for long answers and HOTS, and 10 minutes for the case study.

Are the answers provided with explanations?+

Yes, a comprehensive answer key with brief explanations and working is provided at the end of the worksheet. Each answer includes reasoning, theorem references, and step-by-step calculations where applicable, helping you learn from mistakes and reinforce correct methods.

Is this worksheet aligned with the latest CBSE syllabus and exam pattern?+

Absolutely. This worksheet is based on the NCERT Class 9 Mathematics textbook Chapter 5 'I'm Up and Down, and Round and Round' and follows the latest CBSE exam pattern, including MCQs, short answers, long answers, HOTS, and case-study questions as per recent board guidelines.

What is the difficulty level of this worksheet?+

The difficulty level is Medium to High, mirroring typical CBSE Class 9 school exams and board-style questions. It includes straightforward recall-based questions as well as HOTS problems requiring multi-step reasoning, making it ideal for comprehensive practice and self-assessment.

Can I use this worksheet for last-minute revision before exams?+

Yes, this worksheet is perfect for quick revision. Attempt the MCQs and fill-in-the-blanks to refresh key facts, then solve one or two short-answer and long-answer questions to practice application. Review the answer key to identify and fix gaps in understanding before the exam.

How do I know if I have understood circle properties well?+

If you score above 80 percent on this worksheet and can explain your reasoning for each answer, you have a strong grasp of the chapter. If you struggle with HOTS or case-study questions, revisit the theorems, practice more problems, and consider using CBSETUTOR.ai for personalized step-by-step guidance.

What should I do if I get stuck on a question?+

First, re-read the question and your NCERT textbook section on the relevant theorem. Try drawing a clear diagram and labeling all given information. If still stuck, check the answer key explanation. For deeper doubt-clearing, upload the question to CBSETUTOR.ai and get instant AI-powered step-by-step help anytime, day or night.

Are there more worksheets available for other chapters of Class 9 Mathematics?+

Yes, CBSETUTOR.ai offers free printable worksheets with answers for all chapters of CBSE Class 9 Mathematics and other subjects. Visit the website, browse by chapter, download, print, and practice. You can also access unlimited practice questions and doubt support with a premium subscription.

How does CBSETUTOR.ai help with circle geometry and other Maths topics?+

CBSETUTOR.ai is a 24×7 AI tutor that provides instant step-by-step solutions to any Maths question you upload via photo. It explains theorems, shows working, highlights common mistakes, and suggests practice questions. All CBSE classes 6-12 and subjects are covered for just ₹999 per month, with a 3-day free trial available.

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