Chapter 10 Topics – Practical Geometry of Circles
Click on any topic to expand and view its exercises. Each section includes step-by-step solutions and real-world applications.
10.1 – Circle Constructions
Locating centre, circle through three points, completing arcs
New 2026
This section covers locating the centre of a circle using perpendicular bisectors of chords, constructing a circle through three non-collinear points, and completing a circle from a given arc (with and without finding the centre).
10.1
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Exercise 10.1
Circle constructions & arc completion
10.2 – Tangents to Circles
Tangents from points, tangents meeting at an angle
New 2026
This section covers constructing tangents to circles from points on and outside the circle, tangents to arcs from various positions, and drawing two tangents that meet at a given angle.
10.2
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Exercise 10.2
Tangent constructions & angle problems
Review Exercise 10
Complete revision and mixed practice problems
New 2026
The review exercise mixes questions from both sections of Chapter 10, giving you a chance to test whether you can move between topics without a hint about which method applies — a useful checkpoint before exams.
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Review Exercise 10
Complete Revision & Practice
Practical Geometry of Circles – What's Inside This Chapter (PECTAA 2026)
Chapter 10 – Practical Geometry of Circles is part of Class 10 Mathematics under the Revised National Curriculum 2023. Practical geometry involves constructing circle-related figures. This unit covers geometric constructions involving circles, tangents, and inscribed figures with step-by-step methods for technical drawing, CAD applications, and engineering design.
Prepared by Muhammad Tayyab, Govt Christian High School Daska, this chapter's notes cover all 2 exercises plus the review exercise, with step-by-step solutions throughout.
✅ What This Chapter Covers
- ✓Geometric constructions, tangents, inscribed figures, step-by-step methods
- ✓Step-by-step solved exercises for all 2 sections
- ✓Based on the PECTAA 2026 syllabus
- ✓A complete review exercise for revision
- ✓Free access, no downloads required
🌐 Why This Chapter Matters
Practical geometry involves constructing circle-related figures. This unit covers geometric constructions involving circles, tangents, and inscribed figures with step-by-step methods for technical drawing, CAD applications, and engineering design.
Mastering this chapter builds a foundation for higher studies and board exam success under the PECTAA 2026 syllabus.
Browse Notes by Individual Chapter
Each chapter also has its own dedicated page with exercise cards and full notes.
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Chapter 1: Complex Numbers
Complex number operations, Argand diagrams, and engineering applications with step-by-step solved exercises.
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Chapter 2: Quadratic Equations and Inequalities
Solving techniques, discriminant analysis, optimization applications, and real-world problem solving strategies.
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Chapter 3: Matrices and Determinants
Matrix operations, determinants, inverses, and computer graphics applications with complete solved exercises.
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Chapter 4: Functions and Graphs
Function types, properties, graphing techniques, and scientific applications for comprehensive understanding.
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Chapter 5: Algebraic Fractions
Simplification, operations, solving equations, and engineering applications with detailed step-by-step solutions.
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Chapter 6: Vectors in Plane
Vector operations, dot product, and physics and engineering applications with practical solved problems.
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Chapter 7: Trigonometry
Trigonometric identities, equations, inverse functions, and real-world applications in architecture and navigation.
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Chapter 8: Chords and Arcs of a Circle
Relationships between chords, arcs, angles, and design and engineering applications for circular geometry.
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Chapter 9: Tangent and Angles of a Circle
Tangent properties, angle relationships, and geometry and design applications with construction techniques.
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Chapter 10: Practical Geometry of Circles
Geometric constructions, tangents, inscribed figures, and step-by-step methods for technical drawing.
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Chapter 11: Information Handling
Data collection, graphical representations, statistical analysis, and decision making for real-world problems.
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Chapter 12: Probability
Basic concepts, compound events, conditional probability, and real-world applications in risk assessment.
Explore the Complete Class 10 Math Toolkit
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Class 10 Math Notes Hub
The main hub linking every Class 10 Math chapter in one place.
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Math Key Book
Full solution guide with chapter-wise answers to every textbook question.
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Notes PDF
Downloadable and printable chapter-wise PDF notes for offline study.
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Solved Exercises
Step-by-step worked solutions for every exercise in all 12 chapters.
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Important Questions
Short and long board-focused questions to prioritize your revision.
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Math MCQs
Chapter-wise multiple-choice questions with an online practice test.
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Definitions
Every key term and theorem explained clearly, chapter by chapter.
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Formula Sheet
A quick-revision sheet with all formulas organized by chapter.
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Guess Paper
The latest important chapters and exercises predicted for this year's exam.
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Past Papers
Solved previous board papers with pattern analysis for smarter prep.