Unit 8 Class 10 Math New Book Solutions
Unit 8 Class 10 Math New Book Solutions are available here with complete step-by-step PDF solutions for all exercises of the new Punjab Textbook Board Mathematics book. These solutions are prepared according to the latest 2026–2027 syllabus and follow the official answer key to ensure accuracy.
Unit 8 Class 10 Math New Book Solutions Exercise Wise
Quick Overview of Unit 8 Class 10 Math New Book Solutions
Unit 8 introduces students to Chords and Arcs of a Circle and the relationships between chords, arcs, radii, diameters, and the centre of a circle.
The unit covers:
- Chords of a circle.
- Arcs of a circle.
- Perpendicular from the centre to a chord.
- Equal chords and equal arcs.
- Chords equidistant from the centre.
- Angles subtended by equal chords.
- Applications of circle geometry in practical situations.
What Is Unit 8 Class 10 Math New Book About?
Unit 8, Chords and Arcs of a Circle, focuses on important geometrical properties of circles, especially those involving chords and arcs. Students learn how the centre of a circle is related to its chords and how equal chords, equal arcs, and equal distances from the centre are connected.
The chapter begins with the theorem that a perpendicular drawn from the centre of a circle to a chord bisects that chord. Students then study the converse of this theorem and explore how equal chords are always equidistant from the centre.
Later in the chapter, students learn that equal chords subtend equal angles at the centre and intercept equal arcs. These relationships form the foundation for solving many practical geometry problems involving wheels, circular parks, fountains, clocks, circular tracks, ponds, and fountains.
Solutions of Exercise 8.1 Class 10 Math New Book
Exercise 8.1 introduces the relationship between the centre of a circle and its chords.
Main Topics Covered
- Perpendicular from centre to chord.
- Chord bisecting theorem.
- Finding chord lengths.
- Finding radii using Pythagoras theorem.
- Distance of a chord from the centre.
- Practical applications involving circles.
Students frequently use right triangles and Pythagoras theorem to solve these problems.
Solutions of Exercise 8.2 Class 10 Math New Book
Exercise 8.2 focuses on equal chords, equal arcs, and central angles.
Main Topics Covered
- Equal chords.
- Equal arcs.
- Central angles.
- Congruent arcs.
- Relationships between chords and arcs.
- Practical applications of equal chords and arcs.
Students learn that equal chords subtend equal angles at the centre and intercept equal arcs.
Solutions of Review Exercise 8 Class 10 Math New Book
The review exercise combines all concepts studied throughout the chapter and helps students prepare for examinations.
Main Topics Covered
- MCQs.
- Chords and arcs.
- Central angles.
- Equal chords.
- Distances from the centre.
- Practical applications of circle geometry.
Important Formulas of Unit 8
Chord Bisecting Theorem
A perpendicular drawn from the centre of a circle to a chord bisects the chord.
Converse of Chord Bisecting Theorem
The perpendicular bisector of a chord always passes through the centre of the circle.
Equal Chords Property
Equal chords of the same circle are equidistant from the centre.
Equal Arcs Property
Equal chords intercept equal arcs and equal arcs subtend equal angles at the centre.
Pythagoras Theorem
\[
a^2+b^2=c^2
\]
This formula is frequently used to calculate radii, chord lengths, and distances from the centre.
Common Mistakes in Unit 8
Students often make the following mistakes:
- Forgetting that the perpendicular from the centre bisects the chord.
- Using the entire chord instead of half of the chord in calculations.
- Confusing arcs with chords.
- Assuming unequal chords subtend equal angles.
- Forgetting to apply Pythagoras theorem correctly.
- Mixing major arcs and minor arcs.
- Using incorrect distances in right triangle calculations.
Related Class 10 Math Resources
- Unit 1 Class 10 Math New Book Solutions
- Unit 2 Class 10 Math New Book Solutions
- Unit 3 Class 10 Math New Book Solutions
- Unit 4 Class 10 Math New Book Solutions
- Unit 5 Class 10 Math New Book Solutions
- Unit 6 Class 10 Math New Book Solutions
- Unit 7 Class 10 Math New Book Solutions
Frequently Asked Questions
What happens when a perpendicular is drawn from the centre of a circle to a chord?
The perpendicular bisects the chord into two equal parts.
Do equal chords always have equal distances from the centre?
Yes. Equal chords in the same circle are always equidistant from the centre.
Can three non-collinear points determine a circle?
Yes. Exactly one circle passes through three non-collinear points.
Are equal arcs always subtended by equal chords?
Yes. Equal arcs are subtended by equal chords and vice versa.
Are these solutions according to the new Punjab textbook?
Yes. These solutions follow the latest Punjab Textbook Board Class 10 Mathematics book for the 2026–2027 session.
Disclaimer
These notes and solutions are prepared for educational purposes to help students understand mathematical concepts and methods. Students are encouraged to attempt questions themselves before consulting the solutions.
Final Words
Unit 8, Chords and Arcs of a Circle, is an important geometry chapter because it develops a deeper understanding of the relationships between chords, arcs, and the centre of a circle. The concepts learned in this unit are widely used in engineering, architecture, design, surveying, and advanced mathematics. A strong understanding of chords and arcs also helps students prepare for future geometry topics in higher classes.
