Class 10 Maths Chapter 8 Review Exercise Solutions 2026 – Chords and Arcs of a Circle Notes PDF
Unit 8: Chords and Arcs of a Circle | Review Exercise | Punjab Board New Syllabus 2026–27
Updated August 2026: Review Exercise solutions for Chords and Arcs of a Circle have been uploaded below and are free to view or download, fully solved according to the new PCTB/PECTAA Class 10 Mathematics syllabus.
Testing the Whole Chapter at Once
Exercise 8.1 focused on chord theorems, and Exercise 8.2 turned to arc-angle relationships. The Review Exercise removes those labels and mixes both sets of theorems together, the way a real board paper naturally combines chord and arc reasoning inside a single question.
What This Review Exercise Draws On
Chord Theorems
Quick-recall and applied questions on the perpendicular bisector theorem, equal chords, and distance from the center, exactly as introduced in Exercise 8.1.
Arc and Central Angle Relationships
Mixed problems calculating arc length, applying the equal-arcs/equal-angles theorem, and working with major and minor arcs, as covered in Exercise 8.2.
Combining Chord and Arc Reasoning
Some questions in this review require recognizing that a chord’s properties and its corresponding arc’s properties are linked — for instance, using an equal-chords result to conclude something about the arcs they cut off.
Step-by-Step Solved Examples
Q. No. 1: A chord of length 30 cm is drawn in a circle of radius 17 cm. Find its distance from the center, then find the arc length for a central angle of 60° in the same circle. (Use π = 22/7)
Half chord = 15 cm
d² = 17² − 15² = 289 − 225 = 64 → d = 8 cm
Arc length = (60/360) × 2 × (22/7) × 17 = (1/6) × (748/7)
= 748/42 ≈ 17.8 cm
Q. No. 2: Two equal arcs of a circle correspond to central angles of (2x)° and (x+30)°. Find x, then state the common central angle.
Since the arcs are equal, their central angles are equal:
2x = x + 30
x = 30
Common central angle = 2(30) = 60°
Q. No. 3: In a circle, a chord subtends a minor arc with central angle 140°. State the central angle of the major arc, and explain what this tells you about the chord’s position relative to the center.
Major arc angle = 360 − 140 = 220°
Since the minor arc’s angle (140°) is less than 180°, the chord does not pass through the center — it is not a diameter.
These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of the Review Exercise in the same numbered, step-by-step format.
MCQs, Short Questions & Long Questions from This Review
Alongside the main exercise, this page’s uploaded notes are organized the way Punjab Board papers are structured, so students can practice by question type:
- MCQs: Rapid-fire recall across both exercises, useful for timed practice
- Short Questions: Two-step problems combining any two of the chapter’s core ideas
- Long Questions: Full multi-part problems that mirror the structure of an actual board exam question
Study Tips for Reviewing This Chapter
- Attempt the Review Exercise only after completing Exercises 8.1 and 8.2
- Keep the chord and arc theorems written together on one page — they mirror each other closely and are easy to confuse if studied separately
- Practice sketching a quick diagram for every question, even short ones, to avoid labeling errors
- Re-attempt any question you got wrong the next day, rather than only reading the correct answer once
Common Mistakes Students Make in This Review Exercise
- Trying to answer a multi-step question in one line instead of solving it stage by stage
- Applying a chord theorem where an arc theorem is needed, or vice versa
- Forgetting that a diameter is a chord too, and passes through the center (making its own perpendicular distance zero)
Why This Exercise Matters for the Board Exam
Board papers rarely test chord or arc theorems in complete isolation, which is exactly what this Review Exercise simulates. Working through it carefully is one of the best ways to confirm genuine readiness for Chapter 8 before moving on to Chapter 9.
Quick Links – Chapter 8: Chords and Arcs of a Circle
| Section | Covers |
| Exercise 8.1 | Chord theorems |
| Exercise 8.2 | Arc length & central angles |
| Short Questions | Single-concept practice |
| Chapter 8 MCQs | Objective-type practice |
| Review Exercise | You are here |
Links for sections other than the Review Exercise will be activated as they are published on this site.
Download Review Exercise Notes PDF
Click below to view or download the complete Review Exercise notes in PDF format.
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Frequently Asked Questions (FAQs)
Q1. Are these Review Exercise notes free to download?
Yes, all notes on this page are completely free to view and download in PDF format.
Q2. Which board are these notes for?
These notes are prepared according to the Punjab Board syllabus and are useful for all Punjab boards (Lahore, Gujranwala, Multan, Sargodha, Rawalpindi, Faisalabad, DG Khan, Bahawalpur, Sahiwal) as well as the Federal Board (FBISE).
Q3. When should I attempt the Review Exercise?
Only after completing both exercises (8.1 and 8.2), since the questions here mix chord and arc topics without labeling which exercise each one came from.
Q4. Does this page include MCQs and short questions too?
Yes, the uploaded notes include MCQs, short questions, and long questions covering the whole chapter, organized by question type to match the board paper pattern.
Q5. How can I download the PDF?
Click the “Download PDF” button above and the notes will open or download directly to your device.
Q6. Are these notes updated for the new 2026–27 syllabus?
Yes, these notes are prepared strictly according to the latest PCTB/PECTAA syllabus for the 2026–27 academic session.
Comments & Feedback
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