Circles
Uttarakhand Board · Class 9 · Mathematics
Summary of Circles for Uttarakhand Board Class 9 Mathematics. Key concepts, important points, and chapter overview.
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Circles are one of the most important geometric shapes in mathematics. This chapter explores the relationship between chords, angles, and arcs in circles. We learn about angles subtended by chords at different points, properties of perpendiculars from center to chords, equal chords and their distanc
Key Concepts
When a chord PQ is drawn
When a chord PQ is drawn in a circle, it creates angles at different points. The angle POQ at center O is called angle subtended by chord at center. A
When a perpendicular is drawn from
When a perpendicular is drawn from center of circle to any chord, it bisects that chord (divides it into two equal parts). Conversely, if a line from
Distance of a chord from center
Distance of a chord from center is the length of perpendicular from center to the chord. Equal chords of a circle are equidistant from center (same di
An arc subtends an angle at
An arc subtends an angle at center equal to the angle subtended by corresponding chord. The key theorem states: angle subtended by arc at center is do
All angles subtended by same arc
All angles subtended by same arc at different points on same side of chord are equal. This means if points A and C are on same side of chord PQ, then
Learning Objectives
- Understand the concept of angles subtended by chords at center and other points on circle
- Learn properties of perpendiculars from center to chords
- Explore relationship between equal chords and their distances from center
- Study angles subtended by arcs at center and points on circle
- Understand properties of cyclic quadrilaterals
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