Class 10 Maths Chapter 10 Review Exercise Solutions 2026 – Practical Geometry of Circles Notes PDF
Unit 10: Practical Geometry of Circles | Review Exercise | Punjab Board New Syllabus 2026–27
Updated August 2026: Review Exercise solutions for Practical Geometry of Circles 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 10.1 focused on constructing circles around and inside triangles, and Exercise 10.2 turned to constructing tangent lines. The Review Exercise removes those labels and mixes both sets of constructions together, the way a real board paper naturally combines them inside a single practical question.
What This Review Exercise Draws On
Triangle-Circle Constructions
Quick-recall and applied questions on constructing the circumcenter and incenter of a triangle, exactly as introduced in Exercise 10.1.
Tangent Constructions
Mixed problems constructing a tangent at a point on a circle, or from an external point, as covered in Exercise 10.2.
Combining Construction and Calculation
Some questions in this review require both performing (or describing) a construction and calculating an expected length or angle to verify it — combining the practical and theoretical sides of the chapter.
Step-by-Step Solved Examples
Q. No. 1: Describe how to construct the circumcircle of a right-angled triangle, and state where its center will lie.
Construct the perpendicular bisectors of any two sides; their intersection is the circumcenter.
For a right-angled triangle specifically, the circumcenter always lies exactly at the midpoint of the hypotenuse — a special case worth remembering.
Q. No. 2: A tangent is constructed from an external point 20 cm from the center of a circle of radius 12 cm. Find the expected tangent length, and describe the first construction step.
tangent² = 20² − 12² = 400 − 144 = 256
tangent = 16 cm
First step: join the center O to the external point P, then bisect OP to find its midpoint.
Q. No. 3: Explain why the incenter of any triangle always lies inside the triangle, while the circumcenter does not always lie inside.
The incenter is equidistant from all three sides, and since the angle bisectors always stay within the triangle’s interior, their intersection must also lie inside.
The circumcenter is equidistant from all three vertices, but for an obtuse triangle, the perpendicular bisectors intersect outside the triangle, placing the circumcenter outside too.
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 10.1 and 10.2
- Practice each construction physically with a real ruler and compass — reading the steps alone isn’t enough for this chapter
- Memorize the special case: in a right-angled triangle, the circumcenter is always the midpoint of the hypotenuse
- 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 triangle-circle construction where a tangent construction is needed, or vice versa
- Forgetting the special circumcenter case for right-angled triangles, and constructing it the long way unnecessarily
Why This Exercise Matters for the Board Exam
Board papers rarely test construction methods in complete isolation, which is exactly what this Review Exercise simulates. Working through it carefully, with real construction practice, is one of the best ways to confirm genuine readiness for Chapter 10 before moving on to Chapter 11.
Quick Links – Chapter 10: Practical Geometry of Circles
| Section | Covers |
| Exercise 10.1 | Circumcircle & incircle constructions |
| Exercise 10.2 | Tangent constructions |
| Short Questions | Single-concept practice |
| Chapter 10 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.
[ Download PDF ] [ View Online ]
(Google Drive / download links to be embedded here.)
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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 (10.1 and 10.2), since the questions here mix triangle-circle and tangent construction 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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