Class 10 Maths Chapter 8 Exercise 8.2 Solutions 2026 – Chords and Arcs of a Circle Notes PDF

Unit 8: Chords and Arcs of a Circle | Exercise 8.2 | Punjab Board New Syllabus 2026–27

Updated August 2026: Exercise 8.2 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.

From Straight Chords to Curved Arcs

Exercise 8.1 focused on chords — the straight line segments inside a circle. Exercise 8.2 turns to arcs, the curved portions of the circle’s circumference that those chords cut off, and shows how arcs relate to the central angles and chords associated with them.

Key Concepts Covered in Exercise 8.2

Arc Length and Central Angle

The length of an arc is directly proportional to the central angle it subtends: arc length = (θ/360°) × 2πr, where θ is the central angle in degrees and r is the radius. A larger central angle always corresponds to a longer arc.

Equal Arcs and Equal Central Angles

In the same circle (or congruent circles), equal arcs subtend equal angles at the center, and conversely, equal central angles cut off equal arcs. This mirrors the equal-chords theorem from Exercise 8.1.

Equal Arcs and Equal Chords

Following directly from the previous two theorems, equal arcs in the same circle correspond to equal chords, and equal chords correspond to equal arcs — arcs, chords, and central angles all move together consistently.

Major and Minor Arcs

Any chord (other than a diameter) divides a circle into two arcs of different sizes: the minor arc (shorter) and the major arc (longer). The central angle for the minor arc and the reflex angle for the major arc always add up to 360°.

Step-by-Step Solved Examples

Q. No. 1: Find the length of an arc that subtends a central angle of 60° in a circle of radius 21 cm. (Use π = 22/7)

Arc length = (θ/360) × 2πr = (60/360) × 2 × (22/7) × 21

= (1/6) × 2 × 22 × 3 = (1/6) × 132

= 22 cm

Q. No. 2: Two arcs of the same circle subtend angles of 45° and (2x−5)° at the center. If the arcs are equal, find x.

Since the arcs are equal, their central angles must also be equal:

45 = 2x − 5

50 = 2x

x = 25

Q. No. 3: A chord divides a circle so that the minor arc corresponds to a central angle of 80°. Find the angle corresponding to the major arc.

The minor and major arc angles must add up to 360°:

Major arc angle = 360 − 80 = 280°

These three questions are representative samples. The full PDF notes uploaded on this page walk through every question of Exercise 8.2 in the same numbered, step-by-step format.

MCQs, Short Questions & Long Questions from This Exercise

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: Quick questions on identifying whether an angle refers to a minor or major arc
• Short Questions: Calculating arc length given the radius and central angle, like Q. No. 1 above
• Long Questions: Multi-step problems combining equal-arc and equal-angle theorems, like Q. No. 2 above

Where This Matters Beyond This Exercise

The arc-angle relationships established here become essential in the next chapter, Tangent and Angles of a Circle, where angles subtended by arcs at the center and circumference are compared directly. Arc length calculations are also widely used in engineering and design, wherever curved sections of a fixed radius need precise measurement.

Common Mistakes Students Make in Exercise 8.2

• Forgetting to convert the angle fraction correctly — using θ/180 instead of θ/360 in the arc length formula
• Confusing the minor arc’s angle with the major arc’s angle
• Assuming two arcs are equal just because they look similar in a diagram, without checking the central angles
• Using the diameter instead of the radius in the arc length formula

Why This Exercise Matters for the Board Exam

Arc length questions are formulaic and quick once the (θ/360)×2πr formula is memorized, making them a reliable source of marks in the short-question section. Equal-arc reasoning questions, like Q. No. 2, test conceptual understanding of the chapter’s core theorems rather than just calculation.

Quick Links – Chapter 8: Chords and Arcs of a Circle

Links for sections other than Exercise 8.2 will be activated as they are published on this site.

Download Exercise 8.2 Notes PDF

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Frequently Asked Questions (FAQs)

Q1. Are these Exercise 8.2 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. What is the difference between a minor arc and a major arc?

The minor arc is the shorter of the two arcs created when a chord divides a circle, while the major arc is the longer one. Their central angles always add up to 360°.

Q4. Does this page include MCQs and short questions too?

Yes, the uploaded notes include MCQs, short questions, and long questions related to this exercise’s topics, 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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