Circles
Uttarakhand Board · Class 9 · Mathematics
Complete topic list for Circles in Uttarakhand Board Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.
Topics in Circles
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
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
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
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
Key Concepts
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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.
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