NCERT CBSE Class 10th Mathematics Chapter 10: Circles

Safalta Expert Published by: Sylvester Updated Wed, 22 Jun 2022 06:50 PM IST

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NCERT CBSE Class 10th Mathematics Chapter 10: Circles

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The tenth chapter in Mathematics textbook is 'Circles'.


Circle

A circle is a collection of all points in a plane which are at a constant distance from a fixed point.


Centre

The fixed point is called the centre.


Radius

The constant distance from the centre is called the radius.


Chord

A line segment joining any two points on a circle is called a chord.


Diameter

A chord passing through the centre of the circle is called diameter. It is the longest chord.


Tangent

When a line meets the circle at one point or two coincidings The line is known as points, a tangent. The tangent to a circle is perpendicular to the radius through the point of contact.


The topics discussed in this chapter are as follows:

  • Circle and line in a plane
  • Tangent
  • Secant
  • Tangent perpendicular to the radius at the point of contact
  • The number of tangents drawn from a given point
  • Length of a tangent
  • Lengths of tangents drawn from an external point
 

Students can view and download the chapter from the link given below.

Click here to get the complete chapter
NCERT Solutions for Chapter 10: Circles


Also Check

Chapter 1: Real Numbers
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progression
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 11: Constructions
Chapter 12: Areas Related to Circles
Chapter 13: Surface Areas and Volume
Chapter 14: Statistics
Chapter 15: Probability


Check out Frequently Asked Questions (FAQs) for Chapter 10: Circles

A tangent intersects the circle at

One point

A circle can have _____parallel tangents at a single time

two

The length of the tangent from an external point A on a circle with centre O is

Since the tangent is perpendicular to the radius of the circle, then the angle between them is 90º. Thus, OA is the hypotenuse for the right triangle OAB, which is right-angled at B. As we know, for any right triangle, the hypotenuse is the longest side. Therefore the length of the tangent from an external point is always less than the OA.

If a parallelogram circumscribes a circle, then it is a

rhombus

If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is

We know that the sum of the angle between two radii of a circle and the angle between the tangents at the ends of the radii is 180°.

Therefore, the angle between the tangents at the ends of the radii = 180° – 130° = 50°

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