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Circles

Uttarakhand Board · Class 9 · Mathematics

Quick revision notes for Circles — Uttarakhand Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

43 questions23 flashcards5 concepts

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Illustrates a circle with a chord PQ and points R and S on the major and minor arcs respectively. Shows the angle subtended by the chord at the center (POQ), and at points on the major arc (PRQ) and m
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Key Topics to Revise

1

9.1 Angle Subtended by a Chord at a Point

  • An angle subtended by a line segment PQ at point R is ∠PRQ, formed by joining P and Q to R
  • Angle subtended by chord at centre is the angle formed by joining the endpoints of chord to the centre
  • Longer chords subtend larger angles at the centre
2

9.2 Perpendicular from Centre to Chord

  • Perpendicular from centre to any chord bisects the chord
  • Line from centre that bisects a chord is perpendicular to that chord
  • These are converse theorems of each other
3

9.3 Equal Chords and Distance from Centre

  • Distance from point to line is the length of perpendicular from point to line
  • Equal chords are equidistant from the centre
  • Chords equidistant from centre are equal in length
4

9.4 Angle Subtended by Arc - Most Important for Exams

  • Equal chords make congruent arcs and vice versa
  • Angle at centre = 2 × angle at any point on circle (same arc)
  • Angles in same segment are equal

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Full Notes

Key Concepts

When a chord PQ is drawnWhen a perpendicular is drawn fromDistance of a chord from centerAn arc subtends an angle atAll angles subtended by same arc

Frequently Asked Questions

What are the important topics in Circles for Uttarakhand Board Class 9 Mathematics?
Circles covers several key topics that are frequently asked in Uttarakhand Board Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Circles — Uttarakhand Board Class 9 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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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