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.
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
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.