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
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There can be three possibilities for a line on a plane and a circle.
CBSE Notes for Class 10 Maths Chapter 10 Circles | Free PDF Download
CBSE Class 10 Maths Notes of All Chapters:
CBSE CLASS 10 MATHS NOTES CHAPTER 1 REAL NUMBERS
CBSE CLASS 10 MATHS NOTES CHAPTER 2 POLYNOMIALS
CBSE CLASS 10 MATHS NOTES CHAPTER 3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLES
CBSE CLASS 10 MATHS NOTES CHAPTER 4 QUADRATIC EQUATION
CBSE CLASS 10 MATHS NOTES CHAPTER 5 AIRTHMETIC PROGRESSION
CBSE CLASS 10 MATHS NOTES CHAPTER 6 TRIANGLE
CBSE CLASS 10 MATHS NOTES CHAPTER 7 CONTROL AND COORDINATION
CBSE Class 10 Maths Notes Chapter 8 Introduction To Trigonometry
CBSE CLASS 10 MATHS NOTES CHAPTER 9 SOME APPLICATIONS OF TRIGONOMETRY
CBSE Class 10 Maths Notes Chapter 10 Circle
CBSE CLASS 10 MATHS NOTES CHAPTER 11 CONSTRUCTION
CBSE CLASS 10 MATHS NOTES CHAPTER 12 AREAS RELATED TO CIRCLES
CBSE CLASS 10 MATHS NOTES CHAPTER 13 SURFACE AREA AND VOLUMES
CBSE CLASS 10 MATHS NOTES CHAPTER 14 STATISTICS
CBSE CLASS 10 MATHS NOTES CHAPTER 15 PROBABILITY
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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
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.
PT_{1 }= PT_{2}
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:
Some of the frequently asked questions of CBSE Class 10 Notes: 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.
When the two endpoints of its corresponding chord coincide,
The tangent to a circle can be seen as a special case of the secant.
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.