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Here’s the Class 9 Maths – Chapter 9 (Circles) description in English in a simple and clear way 👇


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📘 Chapter 9: Circles (NCERT Class 9 Maths)

🔹 Introduction

In this chapter, we learn about the circle and related concepts.
A circle is a closed curve in which every point is at the same distance from a fixed point.
That fixed point is called the centre, and the constant distance is called the radius.


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🔹 Important Definitions

1. Circle – The set of all points in a plane that are at a fixed distance from a fixed point.


2. Centre – The fixed point from which all points on the circle are equidistant.


3. Radius – The distance from the centre to any point on the circle.


4. Diameter – The longest chord of a circle that passes through the centre.
Formula: Diameter = 2 × Radius


5. Chord – A line segment joining any two points on a circle.


6. Arc – A part of the circumference of a circle.


7. Segment – The region between a chord and the corresponding arc.


8. Sector – The region between two radii and the arc joining their endpoints.


9. Tangent – A line that touches a circle at exactly one point.


10. Secant – A line that cuts the circle at two distinct points.




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🔹 Important Theorems

1. Theorem 9.1:
All radii of a circle are equal.


2. Theorem 9.2:
The perpendicular bisector of a chord passes through the centre of the circle.


3. Theorem 9.3:
Equal chords of a circle are equidistant from the centre, and the chords which are equidistant from the centre are equal in length.


4. Theorem 9.4:
The tangent to a circle is perpendicular to the radius through the point of contact.


5. Theorem 9.5:
The lengths of tangents drawn from an external point to a circle are equal.




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🔹 Key Points

From a point on the circle, only one tangent can be drawn.

From a point outside the circle, two tangents can be drawn.

From a point inside the circle, no tangent can be drawn.
Applications

Circles are seen in daily life: wheels, coins, clocks, etc.

Concepts of circles are used in engineering, architecture, and mechanical design.
Summary

In this chapter, we learned about:

Definition and parts of a circle (centre, radius, chord, diameter, etc.)

Properties and theorems related to chords and tangents

Tangents from an external point

Practical uses of circle geometry



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