Chapter 10 of 14
Syllabus
Circles — Syllabus
Gujarat Board · Class 10 · Mathematics
What Circles covers in Gujarat Board Class 10 Mathematics: 4 topics, for the 2026-27 session. Part of the Gujarat Board Class 10 Mathematics syllabus.
42 questions22 flashcards5 concepts
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4 Topics · Gujarat Board Class 10 Mathematics · 2026-27
Topics in Circles
1
Introduction to Circle-Line Relationships
- A circle is a collection of all points in a plane at a constant distance (radius) from a fixed point (centre)
- When a line and circle are given in a plane, there are exactly three possible relationships
- Non-intersecting line: No common points between line and circle
2
Tangent to a Circle - Properties and Theorems
- At any point on a circle, there exists exactly one tangent
- A tangent is the limiting case of a secant when both intersection points coincide
- The radius through the point of contact is perpendicular to the tangent
3
Number of Tangents from Different Points
- From a point inside the circle: No tangents possible (0 tangents)
- From a point on the circle: Exactly one tangent possible (1 tangent)
- From a point outside the circle: Exactly two tangents possible (2 tangents)
4
Equal Tangent Lengths from External Point
- From any external point, two tangents can be drawn to a circle
- The lengths of these two tangents are always equal
- This property is proven using congruent right triangles
Key Concepts
A line can have three relationshipsA tangent is a lineThe tangent at any pointFrom a point inside the circleThe lengths of two tangents drawn
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What are the important topics in Circles for Gujarat Board Class 10 Mathematics?
Key topics in Circles include Introduction to Circle-Line Relationships, Tangent to a Circle - Properties and Theorems, Number of Tangents from Different Points, Equal Tangent Lengths from External Point. Study these first, then practise questions on each for the Gujarat Board Class 10 board exam.
How should I revise Circles for the Gujarat Board Class 10 board exam?
Learn the core ideas first, then work through the 42 practice questions on Circles. Revise definitions regularly and use flashcards for quick recall before the exam.
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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