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CBSE Notes for Class 10 Maths Chapter 10 Circles

CBSE Notes for Class 10 Maths Chapter 10 Circles

For Class 10 a brief introduction to circles is provided here. For learning the concept of the circles, a complete description of circles is provided here.

A brief introduction to circles

Line in a plane and circle

 

There can be three possibilities for a line on a plane and a circle.

  • The line on a plane and circles can be non-intersecting.
  • The line on a plane and circles can have a single common point and this line touches the circle.
  • When they have two common points then the line cuts the circle.

 

CBSE Notes for Class 10 Maths Chapter 10 Circles | Free PDF Download

 

Tangent

A line that touches the circle at exactly one point is known as a tangent to a circle. There is a unique tangent passing through it, For every point on the circle.

Secant

A line that has two points in common with the circle is known as a secant to a circle. For forming a chord of the circle, it cuts the circle into two points. 

The special case is secant tangent

When the two endpoints of its corresponding chord coincide,

The tangent to a circle can be seen as a special case of the secant.

At most for a given decent two parallel tangents

There are exactly two segments that are parallel to it, for every given secant of a circle that also touches the circle at two diametrically opposite points.

At the point of contact tangent perpendicular to the radius

Theorem: The theorem states that passing through the point of contact the tangent to the circle at any point is perpendicular to the radius of the circle.

 

From a given point the number of tangents drawn

  1. i) The point will be a secant when any line through that point and the point is in an interior region of the circle.

From the point present inside the circle, no tangent can be drawn to a circle that passes through that point.

ii)There is exactly one tangent to a circle that passes through it when the point of tendency is present in the circle. 

iii)There are accurately two tangents to a circle through it, When the point is present outside of the circle.

 

Length of a tangent

The segment of the tangent from the external point P to the point of tangency I with the circle is used to define the length of the tangent from the point (Say P) to the circle, Where PI is the length of a tangent.

From an external point, the length of the tangent drawn

Theorem: When the tangent is drawn from an external point to a circle the two tangents are of equal length.

PT1 = PT2

Two important theorems in Class 10 Maths Chapter 10 Circles are given below: 

Theorem 10.1: Through the point of contact the tangent at any point of a circle is perpendicular to the radius.

Theorem 10.2: From an external point to a circle the lengths of tangents drawn are equal.

 

About Circles and their properties some interesting facts are listed below:

  • A diameter of a circle is parallel when the tangents are drawn at the ends of the circle.
  • When parallelogram circumscribing a circle is known as a rhombus.
  • Through the center, The perpendicular at the point of contact to the tangent to a circle pass.
  • A quadrilateral subtends supplementary angles at the centre of the circle when the opposite sides of a quadrilateral circumscribe a circle.
  • The chord of the larger circle, which touches the smaller circle, is bisected at the point of contact, In two concentric circles.
  • The lines segment joining the points of contact at the centre is supplementary to the angle subtends by the angle between the two tangents drawn from an external point to a circle.

 

Some of the frequently asked questions of CBSE Class 10 Notes: Chapter 10 Circles

  1. What are the two important theorems in Class 10 Maths Chapter 10 Circles?

Two important theorems in Class 10 Maths Chapter 10 Circles are given below:

Theorem 10.1 Through the point of contact the tangent at any point of a circle is perpendicular to the radius.

Theorem 10.2 From an external point to a circle the lengths of tangents drawn are equal.

 

  1. What is the special case of secant?

 When the two endpoints of its corresponding chord coincide,

The tangent to a circle can be seen as a special case of the secant.

 

  1. What do you understand about tangents? 

A line that touches the circle at exactly one point is known as a tangent to a circle. There is a unique tangent passing through it, For every point on the circle.

 

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